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

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#### Solution

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)

Concept: Criteria for Congruence of Triangles

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