Question

for class 9th intelligent student .
give quick and I will mark u barinlest ans​

Answer 1

Answer:

Given :

ABCD is quadrilateral in which P, Q, R and S are the midpoint of side AB, BC, CD and DA respectively.

To Prove :

PQRS is a parallelogram.

Construction :

Join A and C.

Proof :

In ∆ABC , P and Q are the midpoints of sides AB and BC respectively.

PQ || AC and PQ =1/2 AC ..... (1)

In ∆ADC , R and S are the midpoints of CD and AD respectively.

RS || AC and RS =1/2 AC ..... (2)

From (1) and (2), we have

PQ = RS and PQ || RS

Thus, in quadrilateral PQRS one pair of opposite sides are equal and parallel.

Hence, PQRS is a parallelogram.