Question

1. In quadrilateral ACBD,
AC = AD and AB bisects ZA
(see Fig. 7.16). Show that ABC ABD.
What can you say about BC and BD?
D​

Answer 1

given; AC=AD [1]

AB  bisects angle A

i.e angle CAB =angle BAD   [2]

solution; in triangle ABC and ABD

AB= AB [common]

angle CAB=angle DAB  [2]

AC=AD   [1]

therefor triangle ABC is congruent to triangle ABD by SAS rule

therefor BC=BD  which implies BC and BD are of equal length.

Answer 2

Question :-

In quadrilateral ACBD, AC = AD and AB bisects ∠ A (see figure). Show that ∆ABC ≅ ∆ABD. What can you say about BC and BD?

Answer :-

In quadrilateral ACBD, we have AC = AD and AB being the bisector of ∠A.

Now, In ∆ABC and ∆ABD,

AC = AD (Given)

∠ CAB = ∠ DAB ( AB bisects ∠ CAB)

and AB = AB (Common)

∴ ∆ ABC ≅ ∆ABD (By SAS congruence axiom)

∴ BC = BD (By CPCT)

Plz mrk as brainliest ❤