Question

The midpoints of the adjacent sides of a quadrilateral will form a__________.​

• A. parallelogram​
• B. square
• C. rectangle
• D. trapezium

Answer 1

The correct option is A

parallelogram​

Let ABCD be the quadrilateral and let P, Q, R and S be the midpoints of sides AB, BC, CD and DA respectively.

In ∆CDB, RQ ll DB and RQ = $\frac{1}{2}$ DB (By mid point theorem)

In ∆ ADB, SP ll DB and SP = $\frac{1}{2}$ DB ( By mid point theorem)

Combining these two, RQ ll SP and RQ ll SP

Since a pair of opposite sides are equal and parallel, we can say that PQRS is a parallelogram.