CBSE Class 10 Maths (Basic) 2024 · Paper 430(B) · Question 34(b)

Triangles 5 marks Hard

A B C D

is a trapezium with

A B ∥ D C

and the diagonals intersect each other at the point

O

. Show that

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

Answer

Since

△ A O B \sim △ C O D

(AA),

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

, so

A O \times D O = B O \times C O

and

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

. Hence proved.

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