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In the adjoining figure, D is the mid-po...

In the adjoining figure, D is the mid-point of BC. If BM and CN are perpendiculars from B and C respectively on AD and AD produced, then prove that BM = CN.

Text Solution

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Given : `DeltaABC` in which D is the mid-point of BC, `BM bot AD` and `CN bot AD`
To Prove : `BM=CN`
Proof : In `DeltaBMD` and `DeltaCND`,
`:' {(angleBMD=angleCND,("each "90^(@)", given")),(angleBDM=angleCDN,"(vertically opposite angle)"),(BD=CD,"(given)"):}`
`:' DeltaBMD cong DeltaCND` (AAS)
`implies BM=CN` (c.p.c.t) Hence Proverd.
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