Question

in quadrilateral ABCD ,AC=AD and AB bisect angel A . show that ∆ ABC=∆ABD . what can you say about BC and BD

Answer 1

ABCD is a quadrilateral.
In triangle ABC & triangle ABD,
AC=AD (given)
<BAC=<BAD (as it is given that AB bisects <A)
AB is common
Therefore, triangle ABC =triangle ABD
BC=BD (by CPCT)

Hope it may help you....

Answer 2

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.]