Question

2. In the given figure the sides BA and CA have been produced such that BA = AD
and CA = AE. Prove that DE || BC.​

Answer 1

Answer:

EA=AC [Given]

AD=AB [Given]

∠EAD=∠BAC [Vertically opposite angles]

So, by SAS congruence criterion, we obtain

ΔEAD≅ΔCAB

⇒∠AED=∠ACB and ∠ADE=∠ABC

⇒∠CED=∠ECB and ∠BDE=∠ABC

Hence, DE∥BC