CBSE Class 10 Maths (Basic) 2025 · Paper 430/6/1 · Question 22

Triangles 2 marks Medium

In a trapezium

A B C D

A B ∥ D C

and its diagonals intersect at

O

. Prove that

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

Answer

△ O A B

and

△ O C D

∠ O A B = ∠ O C D

and

∠ O B A = ∠ O D C

(alternate angles,

A B ∥ D C

), so

△ O A B \sim △ O C D

(AA). Hence

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

. Hence proved.

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