Mathematics
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
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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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