Question

In the given figure, AD = CD and AB = CB. Prove that:
1. triangle ABD congruent to
Triangle CBD
2. BD bisects <ABC


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Answer 1

GIVEN,

AD = CD

AB = CB

Prove : ΔABD≅ΔCBD

BD bisects ∠ABC.

1. prove ΔABD≅ΔCBD

AD = CD (given)

AB = CB  (given)

BD = BD (common)

hence, ΔABD≅ΔCBD by SSS congruence. (side, side, side)

2. BD bisects ∠ABC.

∠ABD = ∠CBD (corresponding parts of congruent triangles - CPCT)

hence, we can say BD bisects ∠ABC

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