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

Question

KnowledgeBoat · Accepted Answer

Trapezium ABCD is shown in the figure below: In Δ AOB and Δ COD, ∠AOB = ∠COD (Vertically opposite angles are equal) ∠BAO = ∠DCO (Alternate angles are equal) ⇒ Δ AOB ∼ Δ COD (By A.A. axiom) We know that, Ratio of corresponding sides of a similar triangle are proportional. Hence, proved that .

Mathematics

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

Triangles

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