Question

Prove that the line segments joining midpoint of adjacent sides of a quadrilateral form a parallelogram.

Answer 1

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

Let \(\overline{a},\overline{b},\overline{c},\overline{d},\overline{p},\overline{q},\overline{r}\) and s be the position vectors of the points A, B, C, D, P, Q, R and S respectively.

Since P, Q, R and S are the midpoints of the sides AB, BC, CD and DA respectively,

∴ □PQRS is a parallelogram.