Question

In a quadrilateral ABCD, prove that diagonal AC and BD bisect each other at O, given perpendicular BM,DN is drawn to AC such that DN = BM.​

Answer 1

Answer:

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Answer 2

Given: BM perpendicular to AC

DN perpendicular to AC

BM=DN

To prove: AC bisects BD

Proof: In ∆ DON and ∆ BOM

DN=BM (given)

DON=BOM (Vertically opposite angle)

DNO=BMO ( each 90°)

∆DON congruent to ∆BOM(AAS criteria)

BO=DO (c.p.c.t)

so, AC bisects BD

Proved

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