Question

In quadrilateral ACBD, AC AD and AB bisects ∠A (see Fig. 7.16). Show that ΔABC ≅ ΔABD. What can you say about BC and BD?​

Answer 1

Answer:

Step-by-step explanation:

Given: In quadrilateral ABCD,

AC = AD & AB bisects ∠A i.e, ∠CAB = ∠DAB

To prove,

ΔABC ≅ ΔABD

Proof,

In ΔABC 

& ΔABD,

AB = AB (Common)

AC = AD (Given)

∠CAB =

∠DAB

(AB is bisector)

Hence, ΔABC ≅ ΔABD.       

 (by SAS congruence rule)

Then,

BC= BD (by CPCT)

Thus,

BC & BAD are equal

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.]