Question

ABCD is a parallelogram when

Answer 1

R.E.F image 

∴DC∥AB or DC∥AP 

∴DC=21AP... by mid-point theorem 

DC=AB=BP

CB∥AD or CB∥RA

∴CB=21RA... by mid-point theorem  

CB=DA=DR

Let ABCD be a square  (∵ square is also a ∥ gram) 

∴DC=CB=BA=DA

Here, DC=CB

and, DC=21AP...(i)

CB=21AR...(ii)

Comparing (i) and (ii)

⇒21AP=21AR

Multiplying 2 both sides

⇒AP=AR

∴ΔRAP is an isosceles triangle 

Now, 

To show :- AP+AR= Perimeter of ∥gram ABCD

We know that,

Perimeter of ∥ gram ABCD=AB+BC+CD+DA

but =AB+BC=AP and A