In the given figure, ABCD is a quadrilateral. Diagonal BD bisects ∠ B and ∠ D both. Prove that : (i) △ ABD △ CBD (ii)…

CBSE Class 10 Maths PYQ · Triangles · Similarity with Quadrilaterals · 2 Marks · March 2024 · Standard

Solve it yourself first — then press ↓ or tap Show Solution. Use ← → for previous / next question.

1312 Marks · March 2024 · Standard

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

Show SolutionHide Solution↓

Sol. (i) In $\triangle ABD \& \triangle CBD$
$\angle 3 = \angle 4$
$\angle 1 = \angle 2$
$\therefore \triangle ABD \sim \triangle CBD$
(ii) $\triangle ABD \cong \triangle CBD$
$\therefore AB = BC$