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In the adjoining figure, two lines AB and CD intersect each other at the point O such that BC || DA and BC = DA. Show that O is the mid-point of both the line segments AB and CD.

In the adjoining figure, two lines AB and CD intersect each other at the point O such that BC || DA and BC = DA. Show that O is the mid-point of both the line segments AB and CD. Triangles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

Triangles

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Answer

In △BOC and △DOA,

BC = DA (Given).

∠CBO = ∠DAO (Alternate angles)

∠BOC = ∠DOA (Vertically opposite angles)

∴ △BOC ≅ △DOA by ASA axiom.

We know that corresponding parts of congruent triangles are equal.

∴ BO = AO and CO = DO.

Hence, proved that O is the mid-point of AB and CD.

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