Question

The line segments joining the midpoints of the adjacent sides of quadrilateral form ______.

Options

• a parallelogram

• a rectangle

• a square

• a rhombus

Answer 1

The line segments joining the midpoints of the adjacent sides of quadrilateral form a parallelogram.

Explanation:

Let P, Q, R, S be midpoints of AB, BC, CD, DA.

In triangles ABC and ADC, PQ and SR are each parallel to AC, so PQ || SR; similarly PS || QR.

Thus opposite sides are parallel and PQRS is a parallelogram