Question

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

class 7 th math
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Answer 1

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

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Answer 2

the answer is DE = BC

because DE & BC are opposite to each other