Question

In the given figure ∆ABC is an isosceles triangle in which AB=AC. If AB and AC are produced to D and E respectively such that BD= CE, prove that BE=CD.

Answer 1

Hope it helps you out.

Answer 2

Answer: As Δ ADC ≅ Δ AEB so BE= CD

Step-by-step explanation:

In the given figure

Given : AB = AC -----(i)

           BD = CE ------(ii)

Now

(i) +(ii) we get

AB+ BD= AC+ CE

⇒ AD= AE

Now consider Δ ADC and Δ AEB

AC = AB                              (Given)

AD = AE                              (Proved above)

∠A= ∠A                               (Common)

Therefore  Δ ADC ≅ Δ AEB       (Side - Angle- Side)

BE= CD                                       (C.P.C.T)

Hence, we proved the required result