Question

The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a :

A. Parallelogram 

B. Rectangle 

C. Square 

D. Rhombus

Answer 1

Option : (A)

Given that, 

ABCD is a quadrilateral and P, Q, R and S are the mid points of the sides AB, BC, CD and DA respectively 

To prove : 

PQRS is a parallelogram 

Construction : 

Join A with C

Proof : 

In ΔABC,

P and Q are the mid-points of AB and BC respectively 

Therefore, 

PQ ‖ AC and PQ = AC (Mid-point theorem) ...(i)

Again,

In ΔACD,

R and S are mid-points of sides CD and AD respectively 

Therefore, 

SR ‖ AC and SR = AC (Mid-point theorem) ...(ii) 

From (i) and (ii), we get 

PQ ‖ SR and PQ = SR

Hence, 

PQRS is a parallelogram 

(One pair of opposite sides is parallel and equal)