Question

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

Answer 1

It is given that ∠BAD = ∠EAC

∠BAD + ∠DAC = ∠EAC + ∠DAC

∠BAC = ∠DAE

In ΔBAC and ΔDAE,

AB = AD ................(Given)

∠BAC = ∠DAE ...................(Proved above)

AC = AE (Given)

∴ ΔBAC ≅ ΔDAE .............(By SAS congruence rule)

∴ BC = DE (By CPCT)