Question

In the given figure; AB = BC and AD = EC.
Prove that: BD = BE.

Answer 1

In ΔABC,
AB = BC .......(given)
⇒ ∠BCA = ∠BAC  .......(Angles opposite to equal sides are equal)
⇒ ∠BCD = ∠BAE ….(i)
Given, AD = EC
⇒ AD + DE = EC + DE ...(Adding DE on both sides)
⇒ AE = CD .....….(ii)
Now, in triangles ABE and CBD,
AB = BC .....(given)
∠BAE = ∠BCD ....[From (i)]
AE = CD ......[From (ii)]
⇒ ΔABE ≅ ΔCBD
⇒ BE  = BD ....(cpct)