Question

AC=AE, AB=AD and angle BAD=angle EAC show that BC=DE

Answer 1

Given,

AC = AE, AB = AD and ∠BAD =∠EAC

To prove:

BC = DE

Proof: We have

∠BAD =∠EAC

(Adding ∠DAC to both sides) ∠BAD +∠DAC =∠EAC +∠DAC

⇒ ∠BAC = ∠EAD

In ΔABC and ΔADE,

AC = AE (Given)

∠BAC =∠EAD (proved above)

AB = AD (Given)

Hence, ΔABC ≅ ΔADE (by SAS congruence rule)

Then,

BC = DE ( by CPCT.)

Answer 2

Step-by-step explanation:

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