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In the given figure, ABCD is a parallelo...

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that :
(i) `DeltaADN =DeltaCBP`
`(ii) AN=CP`

Text Solution

Verified by Experts

`(i)In DeltaADN and DeltaCBP`
`because{:{(angleAND=angleCBP,(each90^(@))),(AD=CB,("opposite sides of a parallelogram")),(angleADN = angleCVBP,"(alternate angles" AD||BC):}`
`therefore" "DeltaADH~=DeltaCBP" (AAS theorem")`
`(ii) because" "DeltaADN~=DeltaCBP`
`therefore" "AN|CP" "(c.p.c.t)`
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