Question

In the adjacent figure AC= AE , AB= AD and BAD= EAC .Show that BC= DE.

Answer 1

if you still have any doubt then ask.

Answer 2

 

Given,

AC = AE, AB = AD and ∠BAD = ∠EAC

 

To prove:

BC = DE

Proof: We have

∠BAD =

∠EAC

(Adding ∠DAC to both sides)

∠BAD +

∠DAC =

∠EAC +

∠DAC

⇒ ∠BAC = ∠EAD

In ΔABC and ΔADE,

AC = AE (Given)

∠BAC =

∠EAD    (proved above)

AB = AD (Given)

Hence, ΔABC ≅ ΔADE             (by SAS congruence rule)

Then,

BC =DE ( by CPCT.)