Question

ABCD is a parallelogram. AN and CM are perpendiculars drawn on the diagonal BD from A and C respectively. Prove that (a) ΔADN ~= ΔCBM (b) AN=CM.


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Answer 1

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Answer 2

Answer:

In △ADN and △CBP

AD=CB (opposite side of parallelogram)

∠AND=∠CPB (each 90∘)

∠ADN=∠PBC (AD∥BC,BD is transversal) (alternate interior angles)

1. Therefore,△ADN=△CBP (ASA rule)

2. AN=CP (By cpct)

Hence proved.

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