Question

In Fig. it is given that AB = BC and AD = EC. Prove that $\Delta$ABE $\cong$ $\Delta$CBD
[3 MARKS]

Answer 1

Process : 2 Marks
Proof : 1 Mark

In $\Delta$ ABC, we have
BA = BC [Given]
$\Rightarrow$ $\angle$BCA = $\angle$BAC
[Angles opp. to equal sides are equal]
$\Rightarrow$ $\angle$BAE = $\angle$BCD

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

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