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.
​

Answer 1

Step-by-step explanation:

IN triangle ADN and triangle CBM

AD=BC(parallelogram opposite sides equal)

MB=DN (AB=DC,1/2 AB=1/2 DC)

Angle AND=Angle CMB(Right angle)

SO,triangleAND and triangle CBM are congruent

by cpct

AN=CM

Answer 2

Answer:

Solution:

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