Question

AN and CP are perpendiculars to the diagonal bd of a parallelogram abcd prove that ∆adn congruent to ∆cbp andAN=CP

Answer 1

AB is parallel to CO ( opposite sides of parallelogram) 

Therefore angle D = angle B (alt. angles) 


In triangles ADN and CBP 

angleN = angle P ( each 90 degree0 
angle D = angle B ( proved above) 
AD = CB (opposite sides of parallelogram ) 

Triangles ADN and CBP are congruent. (SAS RULE) 

That implies AN = CP (CPCT) 

And areas ADN and COP are equal. ( congruent figures are equal in areas) 

Hence proved