Question

in quadrilateral acbd ac is equal to ad and ab bisects angle A show that triangle ABC is congruent to triangle ABD what can you say about BC andBD

Answer 1

Solutions:

In △ABC and △ABD, we have

AC = AD ........... [Given]

∠CAB = ∠DAB ........ [Since, AB is the bisector of ∠DAC]

and,. AB = AB ............ [Common]

So, by SAS congruence rule, we obtain

△ABC ≅ △ABD

=> BC = BD .......... [By c.p.c.t.]

Answer 2

Given :- In quadrilateral ACBD

AC = AD

AB bisects angle A

To proof :- (i) triangle ABC congruent triangle ABD.

(ii) Relation between BC and BO.

Proof :- (i) In triangle ABC and ABD

angle 1 = angle 2 (given)

AC = AD (given)

AB = AB (common)

Therefore , triangle ABC congruent triangle ABD (SAS).

(ii) BC = BD (cpct).