Question

The line segments joining the mid points of a quadrilateral form a .

• A. square
• B. rhombus
• C. parallelogram
• D. kite

Answer 1

The correct option is C parallelogram

Consider a quadrilateral ABCD. P, Q, R, and S are the mid-points of sides AB, BC, CD and DA respectively. Join AC.

The mid-point theorem states that a line segment joining mid points of two sides of a triangle is parallel to the third side and is half of it.
$⟹SR\parallel AC\parallel PQ$
$⟹SR=PQ=\frac{1}{2}AC$,
Similarly,
SP $\parallel$ RQ
SP = RQ
Opposite sides of quadrilateral PQRS are parallel and equal.
Hence, PQRS is a parallelogram.