Question

In fig. AC = AE, AB = AD and BAD = EAC. Prove that BC = DE.

Answer 1

Step-by-step explanation:

It is given that ∠BAD=∠EAC

∠BAD+∠DAC=∠EAC+∠DAC [add ∠DAC on both sides]

∴∠BAC=∠DAE

In △BAC and △DAE

AB=AD (Given)

∠BAC=∠DAE (Proved above)

AC=AE (Given)

∴△BAC≅△DAE (By SAS congruence rule)

∴BC=DE (By CPCT)