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