Q3 of 49 Page 45

In a triangle ABC, AB = AC. Points E on AB and D on AC are such that AE = AD. Prove that triangles BCD and CBE are congruent.

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In Δ BCD and Δ CBE we have


AB = AC


AE = AD


Subtracting the above two equations we get


AB-AE = AC-AD


⇒ Be = CD


∠EBC = ∠DCB(Base angle of an isosceles triangle)


BC = BC(Common side)


So Δ BCD and Δ CBE are congruent to each other by S.A.S. axiom of congruency.


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