Question

if P Q RS is the mid point of side AB BA CD AND AD prove that area of PORS is half then area of ABCD

Answer 1

Answer:

Data:

A quadrilateral ABCD in which P, Q, R, S are the mid points of sides AB , BC , CD , DA respectively .

AC is the diagonal.

To prove :

SR//AC and SR= ½AC

PQ= SR

PQRS is a parallelogram .

Proof :

In ∆ACD , S is the mid point of AD and R is the mid point of DC .

Hence SR//AC and SR= ½AC -(1)

By Mid point Theorem .

Now , in ∆ ABC , P is the mid point of AB and Q is the mid point of BC .

Hence PQ//AC , PQ =½AC -(2)

By (1)&(2) ,

SR = PQ , SR //PQ -(3)

By (3) we can say that PQRS is a parallelogram .

Hence Proved .

ALL THE BEST DEAR.