In the adjoining figure ABCD is a quadrilateral in which P Q R and S are midpoints of AB BC CD and D...

Question

In the adjoining figure ABCD is a quadrilateral in which P Q R and S are midpoints of AB BC CD and DA respectively AC is its diagonal Show that i SR AC and SR AC ii PQ SR iii PQRS is a parallelogram

Accepted Answer

It is given that

In quadrilateral ABCD

P, Q, R, and S are the mid-points of sides AB, BC, CD, and DA

AC is the diagonal

To find:

(i) SR || AC and SR = ½ AC

(ii) PQ = SR

(iii) PQRS is a parallelogram

Proof:

(i) In Δ ADC

S and R are the mid-points of AD and DC

SR || AC and SR = ½ AC….. (1) Using the mid-point theorem

(ii) In Δ ABC

P and Q are the midpoints of AB and BC

PQ || AC and PQ = ½ AC ….. (2)

Using equation (1) and (2)

PQ = SR and PQ || SR

(iii) PQ = SR and PQ || SR

Hence, PQRS is a parallelogram.

ML Aggarwal Solutions Class 9 Mathematics Solutions for Mid Point Theorem Exercise 11 in Chapter 11 - Mid Point Theorem