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Question

In Fig. it is given that AB = BC and AD = EC. Prove that ΔABE ΔCBD
[3 MARKS]

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Solution

Process : 2 Marks
Proof : 1 Mark

In Δ ABC, we have
BA = BC [Given]
BCA = BAC
[Angles opp. to equal sides are equal]
BAE = BCD

We have, AD = EC
AD + DE = DE + EC [Adding DE on both sides ]
AE = CD..... (ii)

Now, in Δ ABE and CBD, we have
AB = BC [Given]
BAE = BCD [From (i)]
and, AE = CD [From (ii)]
So,
Δ ABE Δ CBD [SAS criterion of congruence]


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