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Solution for Diagonals Ac and Bd of a Trapezium Abcd with Ab || Dc Intersect Each Other at the Point O. Using Similarity Criterion for Two Triangles, Show that `"Oa"/"Oc"="Ob"/"Od"` - CBSE Class 10 - Mathematics

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Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using similarity criterion for two triangles, show that `"OA"/"OC"="OB"/"OD"`

Solution

We have,

ABCD is a trapezium with AB || DC

In ΔAOB and ΔCOD

∠AOB = ∠COD                   [Vertically opposite angles]

∠OAB = ∠OCD                   [Alternate interior angles]

Then, ΔAOB ~ ΔCOD         [By AA similarity]

`therefore"OA"/"OC"="OB"/"OD"`                [Corresponding parts of similar Δ are proportional]

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Solution for question: Diagonals Ac and Bd of a Trapezium Abcd with Ab || Dc Intersect Each Other at the Point O. Using Similarity Criterion for Two Triangles, Show that `"Oa"/"Oc"="Ob"/"Od"` concept: Triangles Examples and Solutions. For the course CBSE
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