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Answer 1

Question: In the given figure, AB = AC, BD = EC. Prove that ΔABE ≅ ΔACD and AD = AE.

Given:

AB = AC

BD = EC

To Prove:

ΔABE ≅ ΔACD

AD = AE.

Proof:

In ΔABC

AB = AC (given)

We know that angles opposite to equal sides are equal, Therefore,

∠ACB = ∠ABC → Eq(1)

ATQ,

BD = EC

Adding DE on both sides we get,

BD + DE = EC + DE

BE = DC → Eq(2)

In ΔABE and ΔACD,

AB = AC (given)

∠ACB = ∠ABC (Proved in Eq.1)

BE = DC (Proved in Eq.2)

∴ ΔABE ≅ ΔACD using SAS Congruency.

Also, we know that corresponding parts of congruent triangles are equal (CPCT), Therefore,

AD = AE (CPCT)

Hence Proved.

Answer 2

Given - AB = AC , BD = EC.d

To Prove - (1) ΔABE ~ ΔACD

(2) AD = AE

Proof - In ΔABE and ΔACD we have ,

AB = AC (opp. side of triangle )

BE = CD

AE = AD

Therefore , ΔABE ~ ΔACD

Hence proved.

And, AD = AE (Proved above )

Hence Proved..

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