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Question

In Fig. AC = AE, AB = AD and BAD = EAC. Prove that BC = DE.
[2 MARKS]

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Solution

Concept : 1 Mark
Proof : 1 Mark

We have,

BAD = EAC

Then,
BAD + DAC = EAC + DAC
[Adding DAC to both sides]

BAC = DAE ---- (i)

Now, In ΔABC and ΔADE,
AB = AD [Given]
BAC = DAE [From (i)]
and, AC = AE [Given]

So,
ΔABC ΔADE [SAS congruence criterion]

BC = DE [ C.P.C.T ]


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