Diagonals AC and BD of trapezium ABCD with AB||DC intersect each other at point O . Show that OA/OC = OB/OD .

CBSE Class 10 Maths PYQ · Triangles · Similarity with Quadrilaterals · 2 Marks · March 2023 · Standard

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1292 Marks · March 2023 · Standard

Diagonals $AC$ and $BD$ of trapezium $ABCD$ with $AB||DC$ intersect each other at point $O$. Show that $\frac{OA}{OC} = \frac{OB}{OD}$.

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In $\triangle AOB$ and $\triangle COD$,
$\angle OAB = \angle OCD$
$\angle OBA = \angle ODC$
Therefore, $\triangle AOB \sim \triangle COD$
$\therefore \frac{OA}{OC} = \frac{OB}{OD}$