In the given figure, ABCD is a quadrilateral. Diagonal BD bisects $\angle B$ and $\angle D$ both. Prove that:
(i) $ riangle ABD \sim riangle CBD$
(ii) $AB = BC$

[IMAGE_1]

Question

In the given figure, ABCD is a quadrilateral. Diagonal BD bisects $\angle B$ and $\angle D$ both. Prove that:
(i) $	riangle ABD \sim 	riangle CBD$
(ii) $AB = BC$

[IMAGE_1]

Accepted Answer

Step 1: (i) In $	riangle ABD$ and $	riangle CBD$:
$\angle 3 = \angle 4$ (BD bisects $\angle D$)
$\angle 1 = \angle 2$ (BD bisects $\angle B$)
$	herefore 	riangle ABD \sim 	riangle CBD$ (AA similarity)
Step 2: (ii) $	riangle ABD \cong 	riangle CBD$ (ASA)
$	herefore AB = BC$ (CPCT)

Question

Solution