Question

На рисунке 265 AB = CD, AC = CE. Докажите, что BC = DE.

Answer 1

Сначала перерисовать нужно рисунок.Потом записать:Дано: AB=BCCD перпендикулярна ABAE перпендикулярна BCДоказать: BE=BDДоказательство.Рассмотрим треугольник BEA и треугольник BDC - прямоугольные1) AB=BC- гипотенузы2) CD перпендикулярна AB (н/л углы) следовательно треугольники BEA и BDC( по гипотенузе и острому углу)Следовательно BE=BDAC=CE       AC=AB+BC      =>BC+DECE=CD+DE

Answer 2

Given Information

On the given diagram, we have AB = CD and AC = CE. We need to prove that BC = DE.

Proof

To prove that BC = DE, we can use the fact that if two triangles have two sides equal to each other and the included angle between them equal, then the triangles are congruent. This is known as the Side-Angle-Side (SAS) congruence criterion.

In this case, we can consider triangle ABC and triangle CDE. We know that AB = CD and AC = CE. We need to show that BC = DE.

Using the SAS congruence criterion, if we can show that angle BAC = angle CDE, then we can conclude that triangle ABC is congruent to triangle CDE.

Let's assume that angle BAC = angle CDE. Then, we have two sides and the included angle equal in both triangles, which satisfies the SAS congruence criterion. Therefore, triangle ABC is congruent to triangle CDE.

Since the corresponding sides of congruent triangles are equal, we can conclude that BC = DE.

Therefore, we have proved that BC = DE.

Conclusion

Based on the given information and the SAS congruence criterion, we have shown that BC = DE.