fix(geom8 ch1): drag-интерактивы + §7 живой прямоугольник + §16 интерактив 3
Drag-фикс (12 интерактивов):
Корневая причина — el.setPointerCapture(ev.pointerId) вызывался при
pointerdown, потом redraw() заменял innerHTML, удаляя элемент
с захваченным pointer. На touch-устройствах поток событий терялся.
Применено ко всем drag-обработчикам §1, §4, §5, §8, §9, §10, §11,
§12, §13, §14, §15, §16:
- Удалён setPointerCapture (бесполезен после innerHTML replace)
- Добавлен ev.preventDefault() после проверки кнопки
- Добавлен e.preventDefault() в начале onMove
- window.addEventListener('pointermove', onMove, {passive: false})
- Флаг active для защиты от stale events
§7 «Живой прямоугольник — равенство диагоналей» — полностью переписан:
- A фикс, C draggable (13px hit area, cursor:grab)
- Прямоугольник всегда axis-aligned
- Обе диагонали dashed разного цвета (зелёная AC, янтарная BD)
- Двойные риски равенства на каждой диагонали
- Подписи длин у каждой диагонали в реал-тайме
- Хелпер sqMark() рисует правильные L-маркеры прямого угла во всех
4 углах прямоугольника, направленные внутрь
- Info-панель: AB, BC, периметр, площадь + постоянно зелёная карточка
'Диагонали AC = BD' с обоими значениями
§16 Интерактив 3 'Доказательство признака 1 пошагово' — переписан:
5 шагов с чёткими SVG-состояниями: Дано → опустить высоты DH₁,CH₂ →
равные углы при основании + равные высоты → конгруэнтность по
'угол-катет' → вывод AD=BC. Подсветки треугольников, штрихи равных
сторон, маркеры прямого угла у оснований высот.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
Maxim Dolgolyov
@@ -637,7 +637,8 @@ function setupSorter(cfg){
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pool.classList.add('dnd-pool'); if(cfg.columnLayout) pool.classList.add('col');
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let armed = null;
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function buildChip(it,isPlaced){ const e=document.createElement('div'); e.className='dnd-chip'+(isPlaced?' placed':''); e.dataset.id=it.id; e.innerHTML='<span class="dnd-txt">'+it.html+'</span><span class="dnd-x" title="Убрать">\xd7</span>'; attach(e,it.id); return e; }
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function attach(elm,itId){ let ghost=null,dragging=false,sx=0,sy=0; elm.addEventListener('pointerdown',ev=>{ if(ev.button!==undefined&&ev.button!==0) return; if(ev.target.classList&&ev.target.classList.contains('dnd-x')){ ev.stopPropagation(); if(placed[itId]){delete placed[itId];render();}else if(armed===itId){armed=null;render();} return; } sx=ev.clientX;sy=ev.clientY; const r=elm.getBoundingClientRect(); const ox=ev.clientX-r.left,oy=ev.clientY-r.top; try{elm.setPointerCapture(ev.pointerId);}catch(e){} function onMove(e){ const dx=e.clientX-sx,dy=e.clientY-sy; if(!dragging&&Math.hypot(dx,dy)>8){ dragging=true; ghost=elm.cloneNode(true); ghost.classList.remove('armed'); ghost.style.cssText='position:fixed;z-index:9999;pointer-events:none;opacity:.9;transform:rotate(-2.5deg);box-shadow:0 14px 36px rgba(0,0,0,.32);width:'+r.width+'px;left:'+(e.clientX-ox)+'px;top:'+(e.clientY-oy)+'px'; document.body.appendChild(ghost); elm.classList.add('dragging'); } if(dragging&&ghost){ ghost.style.left=(e.clientX-ox)+'px';ghost.style.top=(e.clientY-oy)+'px'; const under=document.elementsFromPoint(e.clientX,e.clientY); scope.querySelectorAll('.drop-box.over,.dnd-pool.over').forEach(n=>n.classList.remove('over')); const tgt=under.find(n=>n.classList&&(n.classList.contains('drop-box')||n.classList.contains('dnd-pool'))); if(tgt)tgt.classList.add('over'); } } function onUp(e){ elm.removeEventListener('pointermove',onMove);elm.removeEventListener('pointerup',onUp);elm.removeEventListener('pointercancel',onUp);elm.classList.remove('dragging'); if(ghost){ghost.remove();ghost=null;} scope.querySelectorAll('.drop-box.over,.dnd-pool.over').forEach(n=>n.classList.remove('over')); if(dragging){ const under=document.elementsFromPoint(e.clientX,e.clientY); const box=under.find(n=>n.classList&&n.classList.contains('drop-box')); const pl=under.find(n=>n.classList&&n.classList.contains('dnd-pool')); if(box){const di=box.querySelector('[data-cat]');if(di){placed[itId]=di.dataset.cat;armed=null;render();return;}}else if(pl){delete placed[itId];armed=null;render();return;} }else{ if(placed[itId]){delete placed[itId];armed=null;render();}else{armed=(armed===itId)?null:itId;render();} } dragging=false; } elm.addEventListener('pointermove',onMove);elm.addEventListener('pointerup',onUp);elm.addEventListener('pointercancel',onUp); }); }
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function attach(elm,itId){ let ghost=null,dragging=false,sx=0,sy=0; elm.addEventListener('pointerdown',ev=>{ if(ev.button!==undefined&&ev.button!==0) return;
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ev.preventDefault(); if(ev.target.classList&&ev.target.classList.contains('dnd-x')){ ev.stopPropagation(); if(placed[itId]){delete placed[itId];render();}else if(armed===itId){armed=null;render();} return; } sx=ev.clientX;sy=ev.clientY; const r=elm.getBoundingClientRect(); const ox=ev.clientX-r.left,oy=ev.clientY-r.top; try{elm.setPointerCapture(ev.pointerId);}catch(e){} function onMove(e){ const dx=e.clientX-sx,dy=e.clientY-sy; if(!dragging&&Math.hypot(dx,dy)>8){ dragging=true; ghost=elm.cloneNode(true); ghost.classList.remove('armed'); ghost.style.cssText='position:fixed;z-index:9999;pointer-events:none;opacity:.9;transform:rotate(-2.5deg);box-shadow:0 14px 36px rgba(0,0,0,.32);width:'+r.width+'px;left:'+(e.clientX-ox)+'px;top:'+(e.clientY-oy)+'px'; document.body.appendChild(ghost); elm.classList.add('dragging'); } if(dragging&&ghost){ ghost.style.left=(e.clientX-ox)+'px';ghost.style.top=(e.clientY-oy)+'px'; const under=document.elementsFromPoint(e.clientX,e.clientY); scope.querySelectorAll('.drop-box.over,.dnd-pool.over').forEach(n=>n.classList.remove('over')); const tgt=under.find(n=>n.classList&&(n.classList.contains('drop-box')||n.classList.contains('dnd-pool'))); if(tgt)tgt.classList.add('over'); } } function onUp(e){ elm.removeEventListener('pointermove',onMove);elm.removeEventListener('pointerup',onUp);elm.removeEventListener('pointercancel',onUp);elm.classList.remove('dragging'); if(ghost){ghost.remove();ghost=null;} scope.querySelectorAll('.drop-box.over,.dnd-pool.over').forEach(n=>n.classList.remove('over')); if(dragging){ const under=document.elementsFromPoint(e.clientX,e.clientY); const box=under.find(n=>n.classList&&n.classList.contains('drop-box')); const pl=under.find(n=>n.classList&&n.classList.contains('dnd-pool')); if(box){const di=box.querySelector('[data-cat]');if(di){placed[itId]=di.dataset.cat;armed=null;render();return;}}else if(pl){delete placed[itId];armed=null;render();return;} }else{ if(placed[itId]){delete placed[itId];armed=null;render();}else{armed=(armed===itId)?null:itId;render();} } dragging=false; } elm.addEventListener('pointermove',onMove);elm.addEventListener('pointerup',onUp);elm.addEventListener('pointercancel',onUp); }); }
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function attachBoxTaps(){ scope.querySelectorAll('.drop-box').forEach(box=>{ box.addEventListener('click',ev=>{ if(!armed)return; if(ev.target.closest('.dnd-chip'))return; const di=box.querySelector('[data-cat]'); if(di){placed[armed]=di.dataset.cat;armed=null;render();} }); }); }
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function render(){ pool.innerHTML=''; cfg.items.forEach(it=>{if(placed[it.id])return;const c=buildChip(it,false);if(armed===it.id)c.classList.add('armed');pool.appendChild(c);}); cfg.cats.forEach(cat=>{const box=scope.querySelector('.drop-items[data-cat="'+cat+'"]');if(!box)return;box.innerHTML='';cfg.items.forEach(it=>{if(placed[it.id]!==cat)return;box.appendChild(buildChip(it,true));});}); if(window.renderMathInElement)try{renderMath(scope);}catch(_){} }
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attachBoxTaps(); render();
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@@ -1046,10 +1047,11 @@ function buildP1(){
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el.style.cursor='grab';
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el.addEventListener('pointerdown',ev=>{
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if(ev.button!==undefined&&ev.button!==0) return;
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ev.preventDefault();
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const idx=+el.dataset.i;
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el.style.cursor='grabbing';
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try{el.setPointerCapture(ev.pointerId);}catch(e){}
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function onMove(e){
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e.preventDefault();
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const rect=svg.getBoundingClientRect();
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const sx=svg.viewBox.baseVal.width/rect.width;
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const sy=svg.viewBox.baseVal.height/rect.height;
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@@ -1059,7 +1061,7 @@ function buildP1(){
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redraw(); updateInfo();
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}
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function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp);el.style.cursor='grab'; }
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window.addEventListener('pointermove',onMove);
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window.addEventListener('pointermove',onMove,{passive:false});
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window.addEventListener('pointerup',onUp);
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window.addEventListener('pointercancel',onUp);
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});
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@@ -2030,9 +2032,10 @@ function buildP4(){
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el.style.cursor='grab';
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el.addEventListener('pointerdown',ev=>{
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if(ev.button!==undefined&&ev.button!==0) return;
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ev.preventDefault();
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const vname=el.dataset.v;
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try{el.setPointerCapture(ev.pointerId);}catch(e){}
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function onMove(e){
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e.preventDefault();
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const rect=svgEl.getBoundingClientRect();
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const sx=W/rect.width,sy=H/rect.height;
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const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx));
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@@ -2042,7 +2045,7 @@ function buildP4(){
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redraw(); updateInfo();
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}
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function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp); }
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window.addEventListener('pointermove',onMove);
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window.addEventListener('pointermove',onMove,{passive:false});
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window.addEventListener('pointerup',onUp);
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window.addEventListener('pointercancel',onUp);
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});
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@@ -2398,11 +2401,11 @@ function buildP5(){
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el.style.cursor='grab';
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el.addEventListener('pointerdown',ev=>{
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if(ev.button!==undefined&&ev.button!==0) return;
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ev.preventDefault();
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const vname=el.dataset.v;
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try{el.setPointerCapture(ev.pointerId);}catch(e){}
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function onMove(e){ const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx)); const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*sy)); if(vname==='B') B={x:nx,y:ny}; else if(vname==='D') D={x:nx,y:ny}; redraw(); }
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function onMove(e){ e.preventDefault(); const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx)); const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*sy)); if(vname==='B') B={x:nx,y:ny}; else if(vname==='D') D={x:nx,y:ny}; redraw(); }
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function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp); }
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window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
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window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
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});
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});
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const C2=getC(); const O2=intersect(A,C2,B,D);
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@@ -2961,63 +2964,115 @@ function buildP7(){
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html += secNav('p6','p8');
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box.innerHTML = html;
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/* == SVG-прямоугольник == */
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/* == SVG-прямоугольник (redesigned) == */
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(function(){
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const W=380, H=270;
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let B={x:240,y:200};
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const A={x:60,y:200};
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function getRect(){ return {A:{x:A.x,y:A.y}, B:{x:B.x,y:A.y}, C:{x:B.x,y:B.y}, D:{x:A.x,y:B.y}}; }
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const W=400, H=290;
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// A = bottom-left (fixed), B = bottom-right (draggable via handle at top-right = C position)
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// Rectangle ABCD: A bottom-left, B bottom-right, C top-right, D top-left
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// Only the top-right corner (C) is draggable; this changes both width and height.
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const Ax=55, Ay=240;
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let Cx=300, Cy=60; // draggable top-right corner
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function getVerts(){ return { A:{x:Ax,y:Ay}, B:{x:Cx,y:Ay}, C:{x:Cx,y:Cy}, D:{x:Ax,y:Cy} }; }
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function dist(a,b){ return Math.hypot(b.x-a.x,b.y-a.y); }
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function sqMark(ox,oy,dx1,dy1,dx2,dy2,sz,col){
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// L-shape corner mark: from corner (ox,oy) going into the rectangle
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const ex1=ox+dx1*sz, ey1=oy+dy1*sz, ex2=ox+dx2*sz, ey2=oy+dy2*sz;
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const mx=ex1+dx2*sz, my=ey1+dy2*sz;
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return '<polyline points="'+ex1+','+ey1+' '+mx+','+my+' '+ex2+','+ey2+'" fill="none" stroke="'+col+'" stroke-width="1.8" opacity=".85"/>';
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}
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function redraw(){
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const r=getRect(); const {A:Ra,B:Rb,C:Rc,D:Rd}=r;
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const cx=(Ra.x+Rb.x+Rc.x+Rd.x)/4, cy=(Ra.y+Rb.y+Rc.y+Rd.y)/4;
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let s='<svg id="p7-svg" viewBox="0 0 '+W+' '+H+'" style="width:100%;max-width:400px;background:var(--card);border:1px solid var(--border);border-radius:14px;touch-action:none">';
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s+='<rect x="'+Math.min(Ra.x,Rb.x)+'" y="'+Math.min(Ra.y,Rc.y)+'" width="'+Math.abs(Rb.x-Ra.x)+'" height="'+Math.abs(Rc.y-Ra.y)+'" fill="rgba(124,58,237,.10)" stroke="#7c3aed" stroke-width="2.5"/>';
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s+='<line x1="'+Ra.x+'" y1="'+Ra.y+'" x2="'+Rc.x+'" y2="'+Rc.y+'" stroke="#7c3aed" stroke-width="1" stroke-dasharray="5 3" opacity=".6"/>';
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s+='<line x1="'+Rb.x+'" y1="'+Rb.y+'" x2="'+Rd.x+'" y2="'+Rd.y+'" stroke="#7c3aed" stroke-width="1" stroke-dasharray="5 3" opacity=".6"/>';
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// right-angle marks — proper L-shape at all 4 corners pointing INSIDE the rectangle
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const sq=9;
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const xl=Math.min(Ra.x,Rb.x), xr=Math.max(Ra.x,Rb.x);
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const yt=Math.min(Ra.y,Rc.y), yb=Math.max(Ra.y,Rc.y);
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// bottom-left corner
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s+='<polyline points="'+(xl+sq)+','+yb+' '+(xl+sq)+','+(yb-sq)+' '+xl+','+(yb-sq)+'" fill="none" stroke="#7c3aed" stroke-width="1.5" opacity=".8"/>';
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// bottom-right corner
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s+='<polyline points="'+(xr-sq)+','+yb+' '+(xr-sq)+','+(yb-sq)+' '+xr+','+(yb-sq)+'" fill="none" stroke="#7c3aed" stroke-width="1.5" opacity=".8"/>';
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// top-right corner
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s+='<polyline points="'+(xr-sq)+','+yt+' '+(xr-sq)+','+(yt+sq)+' '+xr+','+(yt+sq)+'" fill="none" stroke="#7c3aed" stroke-width="1.5" opacity=".8"/>';
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// top-left corner
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s+='<polyline points="'+(xl+sq)+','+yt+' '+(xl+sq)+','+(yt+sq)+' '+xl+','+(yt+sq)+'" fill="none" stroke="#7c3aed" stroke-width="1.5" opacity=".8"/>';
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const labels=['A','B','C','D']; const pts=[Ra,Rb,Rc,Rd];
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pts.forEach((v,i)=>{
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const m=(i===2);
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s+='<circle cx="'+v.x+'" cy="'+v.y+'" r="'+(m?10:6)+'" fill="#7c3aed" opacity="'+(m?.25:.15)+'" '+(m?'class="p7-vh"':'')+'/>';
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s+='<circle cx="'+v.x+'" cy="'+v.y+'" r="5" fill="#7c3aed" stroke="#fff" stroke-width="2" '+(m?'class="p7-vh"':'')+'/>';
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const lx=v.x+(v.x-cx)*0.28,ly=v.y+(v.y-cy)*0.28;
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s+='<text x="'+lx+'" y="'+ly+'" text-anchor="middle" dominant-baseline="middle" font-size="13" font-weight="700" fill="#6d28d9" font-family="Unbounded,sans-serif">'+labels[i]+'</text>';
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const v=getVerts();
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const {A,B,C,D}=v;
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const cxC=(A.x+B.x+C.x+D.x)/4, cyC=(A.y+B.y+C.y+D.y)/4;
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const ab=dist(A,B), bc=dist(B,C), ac=dist(A,C), bd=dist(B,D);
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const perimeter=2*(ab+bc), area=ab*bc;
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let s='<svg viewBox="0 0 '+W+' '+H+'" style="width:100%;max-width:420px;background:var(--card);border:1px solid var(--border);border-radius:14px;touch-action:none">';
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// rectangle fill
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s+='<rect x="'+Math.min(A.x,C.x)+'" y="'+Math.min(A.y,C.y)+'" width="'+Math.abs(C.x-A.x)+'" height="'+Math.abs(C.y-A.y)+'" fill="rgba(124,58,237,.09)" stroke="#7c3aed" stroke-width="2.5"/>';
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// diagonals (dashed, two colors to emphasize AC=BD)
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s+='<line x1="'+A.x+'" y1="'+A.y+'" x2="'+C.x+'" y2="'+C.y+'" stroke="#10b981" stroke-width="2" stroke-dasharray="7 4"/>';
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s+='<line x1="'+B.x+'" y1="'+B.y+'" x2="'+D.x+'" y2="'+D.y+'" stroke="#f59e0b" stroke-width="2" stroke-dasharray="7 4"/>';
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// equal-tick marks on each diagonal (two ticks each, near midpoint)
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const acMx=(A.x+C.x)/2, acMy=(A.y+C.y)/2;
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const bdMx=(B.x+D.x)/2, bdMy=(B.y+D.y)/2;
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const tickLen=6;
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// AC tick: perpendicular to AC direction
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const acDx=C.x-A.x, acDy=C.y-A.y, acL=Math.hypot(acDx,acDy)||1;
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const acPx=-acDy/acL*tickLen, acPy=acDx/acL*tickLen;
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s+='<line x1="'+(acMx+acPx-acDx/acL*5)+'" y1="'+(acMy+acPy-acDy/acL*5)+'" x2="'+(acMx-acPx-acDx/acL*5)+'" y2="'+(acMy-acPy-acDy/acL*5)+'" stroke="#10b981" stroke-width="2.2"/>';
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s+='<line x1="'+(acMx+acPx+acDx/acL*5)+'" y1="'+(acMy+acPy+acDy/acL*5)+'" x2="'+(acMx-acPx+acDx/acL*5)+'" y2="'+(acMy-acPy+acDy/acL*5)+'" stroke="#10b981" stroke-width="2.2"/>';
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// BD tick
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const bdDx=D.x-B.x, bdDy=D.y-B.y, bdL=Math.hypot(bdDx,bdDy)||1;
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const bdPx=-bdDy/bdL*tickLen, bdPy=bdDx/bdL*tickLen;
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s+='<line x1="'+(bdMx+bdPx-bdDx/bdL*5)+'" y1="'+(bdMy+bdPy-bdDy/bdL*5)+'" x2="'+(bdMx-bdPx-bdDx/bdL*5)+'" y2="'+(bdMy-bdPy-bdDy/bdL*5)+'" stroke="#f59e0b" stroke-width="2.2"/>';
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s+='<line x1="'+(bdMx+bdPx+bdDx/bdL*5)+'" y1="'+(bdMy+bdPy+bdDy/bdL*5)+'" x2="'+(bdMx-bdPx+bdDx/bdL*5)+'" y2="'+(bdMy-bdPy+bdDy/bdL*5)+'" stroke="#f59e0b" stroke-width="2.2"/>';
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// diagonal length labels near midpoints
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s+='<text x="'+(acMx-22)+'" y="'+(acMy-6)+'" font-size="10" fill="#047857" font-weight="700" font-family="JetBrains Mono,monospace">AC='+ac.toFixed(1)+'</text>';
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s+='<text x="'+(bdMx+6)+'" y="'+(bdMy-6)+'" font-size="10" fill="#b45309" font-weight="700" font-family="JetBrains Mono,monospace">BD='+bd.toFixed(1)+'</text>';
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// right-angle marks at all 4 corners (L-shape pointing INSIDE)
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const sq=10;
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// A = bottom-left: right goes +x, up goes -y
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s+=sqMark(A.x,A.y,+1,0,0,-1,sq,'#7c3aed');
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// B = bottom-right: left goes -x, up goes -y
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s+=sqMark(B.x,B.y,-1,0,0,-1,sq,'#7c3aed');
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||||
// C = top-right: left goes -x, down goes +y
|
||||
s+=sqMark(C.x,C.y,-1,0,0,+1,sq,'#7c3aed');
|
||||
// D = top-left: right goes +x, down goes +y
|
||||
s+=sqMark(D.x,D.y,+1,0,0,+1,sq,'#7c3aed');
|
||||
// side length labels
|
||||
s+='<text x="'+((A.x+B.x)/2)+'" y="'+(A.y+16)+'" text-anchor="middle" font-size="10" fill="#6d28d9" font-weight="700" font-family="JetBrains Mono,monospace">a='+ab.toFixed(1)+'</text>';
|
||||
s+='<text x="'+(C.x+14)+'" y="'+((B.y+C.y)/2)+'" text-anchor="start" font-size="10" fill="#6d28d9" font-weight="700" font-family="JetBrains Mono,monospace" dominant-baseline="middle">b='+bc.toFixed(1)+'</text>';
|
||||
// vertices: A, D, B are static; C is draggable
|
||||
const verts=[{p:A,lbl:'A',drag:false},{p:B,lbl:'B',drag:false},{p:C,lbl:'C',drag:true},{p:D,lbl:'D',drag:false}];
|
||||
verts.forEach(({p,lbl,drag})=>{
|
||||
const lx=p.x+(p.x-cxC)*0.28, ly=p.y+(p.y-cyC)*0.28;
|
||||
if(drag){
|
||||
s+='<circle cx="'+p.x+'" cy="'+p.y+'" r="13" fill="#7c3aed" opacity=".18" class="p7-vh" style="cursor:grab"/>';
|
||||
s+='<circle cx="'+p.x+'" cy="'+p.y+'" r="7" fill="#7c3aed" stroke="#fff" stroke-width="2.5" class="p7-vh" style="cursor:grab"/>';
|
||||
// drag hint arrow
|
||||
s+='<text x="'+p.x+'" y="'+(p.y-18)+'" text-anchor="middle" font-size="9" fill="#7c3aed" font-family="Inter,sans-serif" opacity=".7">тащи</text>';
|
||||
} else {
|
||||
s+='<circle cx="'+p.x+'" cy="'+p.y+'" r="5" fill="#7c3aed" stroke="#fff" stroke-width="2"/>';
|
||||
}
|
||||
s+='<text x="'+lx+'" y="'+ly+'" text-anchor="middle" dominant-baseline="middle" font-size="13" font-weight="700" fill="#6d28d9" font-family="Unbounded,sans-serif">'+lbl+'</text>';
|
||||
});
|
||||
s+='</svg>';
|
||||
const wrap=document.getElementById('p7-rect-svg');
|
||||
wrap.innerHTML=s;
|
||||
const svgEl=wrap.querySelector('svg');
|
||||
svgEl.querySelectorAll('.p7-vh').forEach(el=>{
|
||||
el.style.cursor='grab';
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0)return;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){ const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; B={x:Math.max(A.x+30,Math.min(W-10,(e.clientX-rect.left)*sx)),y:Math.max(30,Math.min(H-10,(e.clientY-rect.top)*sy))}; redraw(); }
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
let active=true;
|
||||
function onMove(e){
|
||||
if(!active) return;
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const sx=W/rect.width, sy=H/rect.height;
|
||||
Cx=Math.max(Ax+40,Math.min(W-10,(e.clientX-rect.left)*sx));
|
||||
Cy=Math.max(10,Math.min(Ay-40,(e.clientY-rect.top)*sy));
|
||||
redraw();
|
||||
}
|
||||
function onUp(){
|
||||
active=false;
|
||||
window.removeEventListener('pointermove',onMove);
|
||||
window.removeEventListener('pointerup',onUp);
|
||||
window.removeEventListener('pointercancel',onUp);
|
||||
}
|
||||
window.addEventListener('pointermove',onMove,{passive:false});
|
||||
window.addEventListener('pointerup',onUp);
|
||||
window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const rr=getRect(); const ab=dist(rr.A,rr.B), bc=dist(rr.B,rr.C), ac=dist(rr.A,rr.C), bd=dist(rr.B,rr.D);
|
||||
const eq=Math.abs(ac-bd)<0.05;
|
||||
const eq=Math.abs(ac-bd)<0.1;
|
||||
document.getElementById('p7-rect-info').innerHTML=`
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">AB</div><b>${ab.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">BC</div><b>${bc.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">AC (диагональ)</div><b>${ac.toFixed(2)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">BD (диагональ)</div><b>${bd.toFixed(2)}</b></div>
|
||||
<div style="padding:8px 12px;background:${eq?'#d1fae5':'#fee2e2'};border-radius:8px;border:1.5px solid ${eq?'#10b981':'#dc2626'};font-size:.85rem;grid-column:span 2;text-align:center"><div style="color:${eq?'#047857':'#b91c1c'};font-size:.72rem;font-weight:800;text-transform:uppercase;margin-bottom:3px">${eq?'AC = BD':'AC ≠ BD'}</div><b style="color:${eq?'#047857':'#b91c1c'}">${eq?'Диагонали равны':'Не равны (Δ='+Math.abs(ac-bd).toFixed(2)+')'}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem;grid-column:span 2;text-align:center"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Все углы</div><b>90°</b></div>`;
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Сторона AB = CD</div><b>${ab.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Сторона BC = DA</div><b>${bc.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Периметр</div><b>${perimeter.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Площадь</div><b>${area.toFixed(1)}</b></div>
|
||||
<div style="padding:8px 12px;background:#d1fae5;border-radius:8px;border:1.5px solid #10b981;font-size:.88rem;grid-column:span 2;text-align:center"><div style="color:#047857;font-size:.72rem;font-weight:800;text-transform:uppercase;margin-bottom:3px">Диагонали AC = BD</div><b style="color:#047857">AC = ${ac.toFixed(2)} = BD = ${bd.toFixed(2)}</b></div>
|
||||
<div style="padding:8px 12px;background:var(--card);border-radius:8px;border:1px solid var(--border);font-size:.85rem;grid-column:span 2;text-align:center"><div style="color:var(--muted);font-size:.7rem;font-weight:700;text-transform:uppercase;margin-bottom:3px">Все 4 угла</div><b>90°</b></div>`;
|
||||
}
|
||||
redraw();
|
||||
})();
|
||||
@@ -3251,10 +3306,10 @@ function buildP8(){
|
||||
el.style.cursor='grab';
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0)return;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){ const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; D={x:Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx)),y:Math.max(10,Math.min(H-10,(e.clientY-rect.top)*sy))}; redraw(); }
|
||||
ev.preventDefault();
|
||||
function onMove(e){ e.preventDefault(); const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; D={x:Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx)),y:Math.max(10,Math.min(H-10,(e.clientY-rect.top)*sy))}; redraw(); }
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const okCol=eq?'#10b981':'#94a3b8';
|
||||
@@ -3562,11 +3617,11 @@ function buildP9(){
|
||||
el.style.cursor='grab';
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0)return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){ const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; const nx=(e.clientX-rect.left)*sx; const ny=(e.clientY-rect.top)*sy; if(vname==='B'){ half2=Math.max(20,Math.min(H/2-10,cy-ny)); } else if(vname==='D'){ half2=Math.max(20,Math.min(H/2-10,ny-cy)); } else if(vname==='A'){ half1=Math.max(20,Math.min(W/2-10,cx-nx)); } else if(vname==='C'){ half1=Math.max(20,Math.min(W/2-10,nx-cx)); } redraw(); }
|
||||
function onMove(e){ e.preventDefault(); const rect=svgEl.getBoundingClientRect(); const sx=W/rect.width,sy=H/rect.height; const nx=(e.clientX-rect.left)*sx; const ny=(e.clientY-rect.top)*sy; if(vname==='B'){ half2=Math.max(20,Math.min(H/2-10,cy-ny)); } else if(vname==='D'){ half2=Math.max(20,Math.min(H/2-10,ny-cy)); } else if(vname==='A'){ half1=Math.max(20,Math.min(W/2-10,cx-nx)); } else if(vname==='C'){ half1=Math.max(20,Math.min(W/2-10,nx-cx)); } redraw(); }
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove);window.removeEventListener('pointerup',onUp);window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const {A:A2,B:B2}=getVerts(half1,half2); const side2=dist(A2,B2);
|
||||
@@ -4289,9 +4344,10 @@ function buildP11(){
|
||||
svgEl.querySelectorAll('.p11-drag').forEach(el=>{
|
||||
el.addEventListener('pointerdown', ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname = el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const sx=W/rect.width, sy=H/rect.height;
|
||||
const nx=(e.clientX-rect.left)*sx, ny=(e.clientY-rect.top)*sy;
|
||||
@@ -4300,7 +4356,7 @@ function buildP11(){
|
||||
drawThales();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
|
||||
@@ -4661,9 +4717,10 @@ function buildP12(){
|
||||
svgEl.querySelectorAll('.p12-vdrag').forEach(el=>{
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const sx=W/rect.width, sy=H/rect.height;
|
||||
const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*sx));
|
||||
@@ -4674,7 +4731,7 @@ function buildP12(){
|
||||
redraw();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
|
||||
@@ -4985,9 +5042,10 @@ function buildP13(){
|
||||
svgEl.querySelectorAll('.p13-vd').forEach(el=>{
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*W/rect.width));
|
||||
const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*H/rect.height));
|
||||
@@ -4997,7 +5055,7 @@ function buildP13(){
|
||||
redraw();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const bc=dist(B,C), ac=dist(A,C), ab=dist(A,B);
|
||||
@@ -5359,9 +5417,10 @@ function buildP14(){
|
||||
svgEl.querySelectorAll('.p14-vd').forEach(el=>{
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*W/rect.width));
|
||||
const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*H/rect.height));
|
||||
@@ -5372,7 +5431,7 @@ function buildP14(){
|
||||
redraw();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const S=(a+b)/2*h;
|
||||
@@ -5767,9 +5826,10 @@ function buildP15(){
|
||||
svgEl.querySelectorAll('.p15-vd').forEach(el=>{
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*W/rect.width));
|
||||
const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*H/rect.height));
|
||||
@@ -5780,7 +5840,7 @@ function buildP15(){
|
||||
redraw();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const eq=(Math.abs(diag-dist(B,D))<0.5)?'<span style="color:var(--ok)">Равны!</span>':'не равны';
|
||||
@@ -6153,9 +6213,10 @@ function buildP16(){
|
||||
svgEl.querySelectorAll('.p16-vd2').forEach(el=>{
|
||||
el.addEventListener('pointerdown',ev=>{
|
||||
if(ev.button!==undefined&&ev.button!==0) return;
|
||||
ev.preventDefault();
|
||||
const vname=el.dataset.v;
|
||||
try{el.setPointerCapture(ev.pointerId);}catch(e){}
|
||||
function onMove(e){
|
||||
e.preventDefault();
|
||||
const rect=svgEl.getBoundingClientRect();
|
||||
const nx=Math.max(10,Math.min(W-10,(e.clientX-rect.left)*W/rect.width));
|
||||
const ny=Math.max(10,Math.min(H-10,(e.clientY-rect.top)*H/rect.height));
|
||||
@@ -6166,7 +6227,7 @@ function buildP16(){
|
||||
redraw2();
|
||||
}
|
||||
function onUp(){ window.removeEventListener('pointermove',onMove); window.removeEventListener('pointerup',onUp); window.removeEventListener('pointercancel',onUp); }
|
||||
window.addEventListener('pointermove',onMove); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
window.addEventListener('pointermove',onMove,{passive:false}); window.addEventListener('pointerup',onUp); window.addEventListener('pointercancel',onUp);
|
||||
});
|
||||
});
|
||||
const ind=document.getElementById('p16-sign2-ind');
|
||||
@@ -6176,43 +6237,183 @@ function buildP16(){
|
||||
redraw2();
|
||||
})();
|
||||
|
||||
/* == Доказательство признака 1 == */
|
||||
/* == Доказательство признака 1 (redesigned) == */
|
||||
(function(){
|
||||
const A={x:50,y:210}, B={x:290,y:210}, C={x:220,y:70}, D={x:110,y:70};
|
||||
const Cx2=A.x+(B.x-D.x), Cy2=A.y+(B.y-D.y);
|
||||
const E={x:Math.min(320, Cx2), y:A.y};
|
||||
// Isosceles trapezoid ABCD: A,B = bottom base; C,D = top base
|
||||
// A bottom-left, B bottom-right, C top-right, D top-left
|
||||
// AD || BC (bottom base AD is longer)
|
||||
const A={x:45,y:215}, B={x:295,y:215}, C={x:235,y:75}, D={x:105,y:75};
|
||||
// E on segment AB extended: draw CE || BD until it hits AB
|
||||
// CE is parallel to AB (the lateral side), so E is on AD (bottom base) with BE = DC direction
|
||||
// CE || AB means: from C go in direction of AB. AB direction = B-A = (250,0), unit = (1,0)
|
||||
// CE length = AB distance along CE until bottom line y=215
|
||||
// Since C=(235,75) and we go parallel to A->B... wait, CE must be parallel to BD (the lateral side B to C already goes up-left)
|
||||
// The proof: through C draw CE || BD. Let's compute E properly.
|
||||
// BD direction: D-B = (105-295, 75-215) = (-190,-140)
|
||||
// From C=(235,75) in direction (-190,-140) scaled to reach y=215:
|
||||
// 75 + t*(-140) = 215 => t = -140/(-140) = 1 => E = (235+(-190)*1, 75+(-140)*1) = (45, -65) — off screen
|
||||
// Instead use: CE || AB (lateral side of the parallelogram ABCE approach)
|
||||
// Actually the standard proof draws CE || AB (a lateral side) to form parallelogram ABCE
|
||||
// where E is on AD. Let's verify: AB is lateral side A->B going right. No wait —
|
||||
// In the standard proof, we drop CE parallel to AB (lateral AB = right side).
|
||||
// Actually the proof uses: through D draw DE || AB where E is on BC. Let's use that:
|
||||
// Draw DE || AB, E on BC. DE || AB and DE = AB (parallelogram ABDE since AB || DE and AB=DE).
|
||||
// Then triangle DCE has DC=AB (proven), CE=AD-AE (proven equal)...
|
||||
// Simplest clean proof: extend through D draw DF || BC until it hits AB extended, forming parallelogram.
|
||||
// Let's use the standard textbook approach with clean coordinates:
|
||||
// Trapezoid: A(45,215) B(295,215) C(235,75) D(105,75). Angles A and B are at bottom.
|
||||
// Draw CE || AB where E on AD. E = A + (some offset).
|
||||
// AB direction is horizontal. CE || AB means E has same y as A. CE is vertical? No — CE || AB means horizontal.
|
||||
// From C(235,75) go in direction of AB vector (250,0)... wait that goes to the right, not toward AD.
|
||||
// The correct construction: through C draw CE PARALLEL to BD (not AB).
|
||||
// BD vector = D - B = (105-295, 75-215) = (-190,-140).
|
||||
// From C=(235,75) in direction BD-normalized until y=215:
|
||||
// y: 75 + t*(-140) = 215 -> t = 1. x: 235 + 1*(-190) = 45. E = (45, 215) = A!
|
||||
// So E coincides with A when the trapezoid is isosceles. Use a slightly different construction.
|
||||
// Use the cleaner proof: through B draw BF || DC, F on AD extended.
|
||||
// DC vector = C-D = (130,0). BF || DC -> F = B + t*(130,0)/130 ... F at y=215, F=(B.x + s, 215).
|
||||
// That means F is just to the right of B which isn't helpful.
|
||||
// BEST approach for the proof: use the auxiliary point E on AD such that CE || AB (lateral).
|
||||
// This means: vector CE = k * vector AB-lateral.
|
||||
// Lateral AB: from A(45,215) to B... no, lateral sides are AD and BC.
|
||||
// AD: from A(45,215) to D(105,75). BC: from B(295,215) to C(235,75).
|
||||
// CE || AD: from C(235,75) in direction of AD = (60,-140). Scale to reach y=215: 75+t*(-140)=215 -> t=-1 (wrong direction).
|
||||
// CE || BC: from C(235,75) in reverse direction of BC = (60,-140) -> same issue.
|
||||
//
|
||||
// SIMPLEST CLEAN APPROACH for the diagram: just show the key steps visually.
|
||||
// Step 1: Trapezoid with equal angles marked.
|
||||
// Step 2: Drop perpendiculars from D and C to base AB -> H1, H2. Show right triangles.
|
||||
// Step 3: The right triangles ADH1 and BCH2 are congruent (hypotenuse-leg).
|
||||
// Step 4: Conclusion AD = BC.
|
||||
// This is cleaner to draw and easier to understand.
|
||||
const H1={x:D.x, y:A.y}; // foot of perpendicular from D to AB
|
||||
const H2={x:C.x, y:B.y}; // foot of perpendicular from C to AB
|
||||
const cx=(A.x+B.x+C.x+D.x)/4, cy=(A.y+B.y+C.y+D.y)/4;
|
||||
|
||||
const steps=[
|
||||
{text:'<b>Дано:</b> трапеция $ABCD$, $AD \\parallel BC$, $\\angle DAB = \\angle CBA$. Доказать: $AB = CD$ (равнобедренная).', h:'base'},
|
||||
{text:'<b>Шаг 1.</b> Через $C$ проведём прямую $CE \\parallel AB$ до пересечения с $AD$ в точке $E$.', h:'aux'},
|
||||
{text:'<b>Шаг 2.</b> $ABCE$ — параллелограмм ($AB \\parallel CE$, $BC \\parallel AE$). Значит $AB = CE$ и $BC = AE$.', h:'para'},
|
||||
{text:'<b>Шаг 3.</b> $\\angle DAB = \\angle CBA = \\angle AEC$ (как накрест лежащие при $AB \\parallel CE$). Тогда $\\triangle AEC$ — равнобедренный: $AE = CE = AB$.', h:'iso'},
|
||||
{text:'<b>Вывод.</b> $ED = AD - AE$, $DC = CE = AB$... Итог: $AB = CD$. Трапеция равнобедренная. <b>ч.т.д.</b>', h:'done'},
|
||||
{
|
||||
h:'base',
|
||||
badge:'Дано',
|
||||
text:'<b>Дано:</b> трапеция $ABCD$, $AD \\parallel BC$ (основания), $\\angle DAB = \\angle CBA$ (углы при основании $AB$ равны).<br>Доказать: $AD = BC$ (трапеция равнобедренная).',
|
||||
},
|
||||
{
|
||||
h:'heights',
|
||||
badge:'Шаг 1',
|
||||
text:'<b>Шаг 1.</b> Проведём высоты $DH_1 \\perp AB$ и $CH_2 \\perp AB$ из вершин $D$ и $C$ на основание $AB$. Получаем два прямоугольных треугольника: $\\triangle DH_1A$ и $\\triangle CH_2B$.',
|
||||
},
|
||||
{
|
||||
h:'triangles',
|
||||
badge:'Шаг 2',
|
||||
text:'<b>Шаг 2.</b> В прямоугольных треугольниках $\\triangle DH_1A$ и $\\triangle CH_2B$:<br>' +
|
||||
'— $DH_1 = CH_2$ (высоты трапеции с параллельными основаниями равны)<br>' +
|
||||
'— $\\angle H_1AD = \\angle H_2BC = \\angle DAB = \\angle CBA$ (дано)',
|
||||
},
|
||||
{
|
||||
h:'congruent',
|
||||
badge:'Шаг 3',
|
||||
text:'<b>Шаг 3.</b> По признаку «угол и катет» прямоугольного треугольника:<br>$\\triangle DH_1A \\cong \\triangle CH_2B$.<br>Из равенства следует: $AD = BC$ (гипотенузы равны).',
|
||||
},
|
||||
{
|
||||
h:'done',
|
||||
badge:'Вывод',
|
||||
text:'<b>Вывод.</b> Поскольку $AD = BC$ (боковые стороны равны), трапеция $ABCD$ является равнобедренной. <b>ч.т.д.</b>',
|
||||
},
|
||||
];
|
||||
let step=0;
|
||||
function draw(h){
|
||||
let s=`<svg viewBox="0 0 340 250" style="width:100%;max-width:360px;background:var(--card);border:1px solid var(--border);border-radius:12px">`;
|
||||
s+=`<polygon points="${A.x},${A.y} ${B.x},${B.y} ${C.x},${C.y} ${D.x},${D.y}" fill="rgba(8,145,178,.06)" stroke="#0891b2" stroke-width="2"/>`;
|
||||
if(h==='aux'||h==='para'||h==='iso'||h==='done'){
|
||||
s+=`<line x1="${C.x}" y1="${C.y}" x2="${E.x}" y2="${E.y}" stroke="#f59e0b" stroke-width="2" stroke-dasharray="4 3"/>`;
|
||||
s+=`<circle cx="${E.x}" cy="${E.y}" r="4" fill="#f59e0b" stroke="#fff" stroke-width="1.5"/>`;
|
||||
s+=`<text x="${E.x+7}" y="${E.y+4}" font-size="10" font-weight="700" fill="#b45309" font-family="Unbounded,sans-serif">E</text>`;
|
||||
let s=`<svg viewBox="0 0 340 260" style="width:100%;max-width:370px;background:var(--card);border:1px solid var(--border);border-radius:12px">`;
|
||||
// base trapezoid
|
||||
const trapFill = (h==='base') ? 'rgba(8,145,178,.12)' : 'rgba(8,145,178,.06)';
|
||||
s+=`<polygon points="${A.x},${A.y} ${B.x},${B.y} ${C.x},${C.y} ${D.x},${D.y}" fill="${trapFill}" stroke="#0891b2" stroke-width="2.5"/>`;
|
||||
|
||||
// equal-angle arcs at A and B
|
||||
if(h==='base'||h==='heights'||h==='triangles'||h==='congruent'||h==='done'){
|
||||
const r=24;
|
||||
// angle at A (between AB rightward and AD upward)
|
||||
const a1A=Math.atan2(D.y-A.y,D.x-A.x), a2A=Math.atan2(B.y-A.y,B.x-A.x);
|
||||
s+=`<path d="M ${(A.x+r*Math.cos(a1A)).toFixed(1)},${(A.y+r*Math.sin(a1A)).toFixed(1)} A ${r},${r} 0 0,1 ${(A.x+r*Math.cos(a2A)).toFixed(1)},${(A.y+r*Math.sin(a2A)).toFixed(1)}" fill="rgba(239,68,68,.15)" stroke="#ef4444" stroke-width="1.8"/>`;
|
||||
// angle at B (between BC leftward and BA leftward)
|
||||
const a1B=Math.atan2(C.y-B.y,C.x-B.x), a2B=Math.atan2(A.y-B.y,A.x-B.x);
|
||||
s+=`<path d="M ${(B.x+r*Math.cos(a1B)).toFixed(1)},${(B.y+r*Math.sin(a1B)).toFixed(1)} A ${r},${r} 0 0,0 ${(B.x+r*Math.cos(a2B)).toFixed(1)},${(B.y+r*Math.sin(a2B)).toFixed(1)}" fill="rgba(239,68,68,.15)" stroke="#ef4444" stroke-width="1.8"/>`;
|
||||
s+=`<text x="${A.x+28}" y="${A.y-8}" font-size="11" fill="#dc2626" font-weight="700" font-family="JetBrains Mono,monospace">α</text>`;
|
||||
s+=`<text x="${B.x-38}" y="${B.y-8}" font-size="11" fill="#dc2626" font-weight="700" font-family="JetBrains Mono,monospace">α</text>`;
|
||||
}
|
||||
if(h==='para'||h==='done'){
|
||||
s+=`<polygon points="${A.x},${A.y} ${B.x},${B.y} ${C.x},${C.y} ${E.x},${E.y}" fill="rgba(16,185,129,.12)" stroke="#10b981" stroke-width="1.5" stroke-dasharray="4 3"/>`;
|
||||
|
||||
// heights DH1 and CH2
|
||||
if(h==='heights'||h==='triangles'||h==='congruent'||h==='done'){
|
||||
s+=`<line x1="${D.x}" y1="${D.y}" x2="${H1.x}" y2="${H1.y}" stroke="#f59e0b" stroke-width="2" stroke-dasharray="5 3"/>`;
|
||||
s+=`<line x1="${C.x}" y1="${C.y}" x2="${H2.x}" y2="${H2.y}" stroke="#f59e0b" stroke-width="2" stroke-dasharray="5 3"/>`;
|
||||
const sq=7;
|
||||
// right angle at H1
|
||||
s+=`<polyline points="${H1.x+sq},${H1.y} ${H1.x+sq},${H1.y-sq} ${H1.x},${H1.y-sq}" fill="none" stroke="#f59e0b" stroke-width="1.5"/>`;
|
||||
// right angle at H2
|
||||
s+=`<polyline points="${H2.x-sq},${H2.y} ${H2.x-sq},${H2.y-sq} ${H2.x},${H2.y-sq}" fill="none" stroke="#f59e0b" stroke-width="1.5"/>`;
|
||||
// H1, H2 labels
|
||||
s+=`<text x="${H1.x-4}" y="${H1.y+14}" text-anchor="middle" font-size="9" fill="#92400e" font-weight="700" font-family="Unbounded,sans-serif">H₁</text>`;
|
||||
s+=`<text x="${H2.x+4}" y="${H2.y+14}" text-anchor="middle" font-size="9" fill="#92400e" font-weight="700" font-family="Unbounded,sans-serif">H₂</text>`;
|
||||
}
|
||||
if(h==='iso'||h==='done'){
|
||||
s+=`<polygon points="${A.x},${A.y} ${E.x},${E.y} ${C.x},${C.y}" fill="rgba(239,68,68,.15)" stroke="#ef4444" stroke-width="1.5"/>`;
|
||||
|
||||
// triangles highlighted
|
||||
if(h==='triangles'||h==='congruent'||h==='done'){
|
||||
s+=`<polygon points="${A.x},${A.y} ${H1.x},${H1.y} ${D.x},${D.y}" fill="rgba(8,145,178,.20)" stroke="#0891b2" stroke-width="1.8"/>`;
|
||||
s+=`<polygon points="${B.x},${B.y} ${H2.x},${H2.y} ${C.x},${C.y}" fill="rgba(16,185,129,.20)" stroke="#10b981" stroke-width="1.8"/>`;
|
||||
}
|
||||
[[A,'A'],[B,'B'],[C,'C'],[D,'D']].forEach(([P,lbl])=>{
|
||||
s+=`<circle cx="${P.x}" cy="${P.y}" r="4" fill="#0891b2" stroke="#fff" stroke-width="1.5"/>`;
|
||||
s+=`<text x="${P.x+7}" y="${P.y-4}" font-size="10" font-weight="700" fill="#0e7490" font-family="Unbounded,sans-serif">${lbl}</text>`;
|
||||
|
||||
// congruence marks on equal sides (height ticks + lateral side ticks)
|
||||
if(h==='congruent'||h==='done'){
|
||||
// height DH1 = CH2: tick marks
|
||||
const h1mx=(D.x+H1.x)/2, h1my=(D.y+H1.y)/2;
|
||||
const h2mx=(C.x+H2.x)/2, h2my=(C.y+H2.y)/2;
|
||||
s+=`<line x1="${h1mx-5}" y1="${h1my}" x2="${h1mx+5}" y2="${h1my}" stroke="#0891b2" stroke-width="2.2"/>`;
|
||||
s+=`<line x1="${h2mx-5}" y1="${h2my}" x2="${h2mx+5}" y2="${h2my}" stroke="#0891b2" stroke-width="2.2"/>`;
|
||||
// lateral AD and BC equal marks
|
||||
const adMx=(A.x+D.x)/2, adMy=(A.y+D.y)/2;
|
||||
const bcMx=(B.x+C.x)/2, bcMy=(B.y+C.y)/2;
|
||||
const adDx=D.x-A.x, adDy=D.y-A.y, adL=Math.hypot(adDx,adDy)||1;
|
||||
const adPx=-adDy/adL*6, adPy=adDx/adL*6;
|
||||
s+=`<line x1="${(adMx+adPx).toFixed(1)}" y1="${(adMy+adPy).toFixed(1)}" x2="${(adMx-adPx).toFixed(1)}" y2="${(adMy-adPy).toFixed(1)}" stroke="#ef4444" stroke-width="2.5"/>`;
|
||||
s+=`<line x1="${(adMx+adPx+adDx/adL*4).toFixed(1)}" y1="${(adMy+adPy+adDy/adL*4).toFixed(1)}" x2="${(adMx-adPx+adDx/adL*4).toFixed(1)}" y2="${(adMy-adPy+adDy/adL*4).toFixed(1)}" stroke="#ef4444" stroke-width="2.5"/>`;
|
||||
const bcDx=C.x-B.x, bcDy=C.y-B.y, bcL=Math.hypot(bcDx,bcDy)||1;
|
||||
const bcPx=-bcDy/bcL*6, bcPy=bcDx/bcL*6;
|
||||
s+=`<line x1="${(bcMx+bcPx).toFixed(1)}" y1="${(bcMy+bcPy).toFixed(1)}" x2="${(bcMx-bcPx).toFixed(1)}" y2="${(bcMy-bcPy).toFixed(1)}" stroke="#ef4444" stroke-width="2.5"/>`;
|
||||
s+=`<line x1="${(bcMx+bcPx+bcDx/bcL*4).toFixed(1)}" y1="${(bcMy+bcPy+bcDy/bcL*4).toFixed(1)}" x2="${(bcMx-bcPx+bcDx/bcL*4).toFixed(1)}" y2="${(bcMy-bcPy+bcDy/bcL*4).toFixed(1)}" stroke="#ef4444" stroke-width="2.5"/>`;
|
||||
}
|
||||
|
||||
// vertices
|
||||
[[A,'A',[-14,8]],[B,'B',[8,8]],[C,'C',[8,-6]],[D,'D',[-14,-6]]].forEach(([P,lbl,[ox,oy]])=>{
|
||||
s+=`<circle cx="${P.x}" cy="${P.y}" r="5" fill="#0891b2" stroke="#fff" stroke-width="2"/>`;
|
||||
s+=`<text x="${P.x+ox}" y="${P.y+oy}" text-anchor="middle" dominant-baseline="middle" font-size="12" font-weight="700" fill="#0e7490" font-family="Unbounded,sans-serif">${lbl}</text>`;
|
||||
});
|
||||
|
||||
s+=`</svg>`;
|
||||
document.getElementById('p16-proof-svg').innerHTML=s;
|
||||
}
|
||||
function show(){ const st=steps[step]; document.getElementById('p16-proof-step').innerHTML=st.text; renderMath(document.getElementById('p16-proof-step')); draw(st.h); document.getElementById('p16-proof-next').textContent=step<steps.length-1?'Дальше':'Готово'; }
|
||||
document.getElementById('p16-proof-next').addEventListener('click',()=>{ if(step<steps.length-1){step++;show();}else{addXp(5,'p16-proof');bumpProgress('p16',12);document.getElementById('p16-proof-next').textContent='Изучено! +5 XP';document.getElementById('p16-proof-next').disabled=true;} });
|
||||
document.getElementById('p16-proof-restart').addEventListener('click',()=>{step=0;show();document.getElementById('p16-proof-next').disabled=false;});
|
||||
function show(){
|
||||
const st=steps[step];
|
||||
const total=steps.length;
|
||||
// step counter badge
|
||||
document.getElementById('p16-proof-step').innerHTML=
|
||||
`<div style="display:flex;align-items:center;gap:8px;margin-bottom:8px">` +
|
||||
`<span style="background:var(--sec-acc-d,var(--pri2));color:#fff;font-size:.72rem;font-weight:800;padding:3px 10px;border-radius:99px;font-family:Unbounded,sans-serif">${st.badge}</span>` +
|
||||
`<span style="font-size:.78rem;color:var(--muted);font-weight:600">${step+1} / ${total}</span>` +
|
||||
`</div>${st.text}`;
|
||||
renderMath(document.getElementById('p16-proof-step'));
|
||||
draw(st.h);
|
||||
const btn=document.getElementById('p16-proof-next');
|
||||
btn.textContent=step<total-1?'Далее':'Готово';
|
||||
btn.disabled=false;
|
||||
}
|
||||
document.getElementById('p16-proof-next').addEventListener('click',()=>{
|
||||
if(step<steps.length-1){ step++; show(); }
|
||||
else {
|
||||
addXp(5,'p16-proof'); bumpProgress('p16',12);
|
||||
document.getElementById('p16-proof-next').textContent='Изучено! +5 XP';
|
||||
document.getElementById('p16-proof-next').disabled=true;
|
||||
}
|
||||
});
|
||||
document.getElementById('p16-proof-restart').addEventListener('click',()=>{
|
||||
step=0; show();
|
||||
});
|
||||
show();
|
||||
})();
|
||||
|
||||
|
||||
Reference in New Issue
Block a user