CBSE Class 10 Maths (Standard) 2024 · Paper 30/1/1 · Question 24

Triangles 2 marks Medium

In the given figure,

A B C D

is a quadrilateral. Diagonal

B D

bisects

∠ B

and

∠ D

both. Prove that :

Quadrilateral ABCD with diagonal BD

Answer

(i)

△ A B D \sim △ C B D

by the AA criterion, since

∠ A B D = ∠ C B D

and

∠ A D B = ∠ C D B

; (ii) The ratio

\frac{A B}{C B} = \frac{B D}{B D} = 1

, so

A B = B C

. Hence proved.

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