Question

P, Q, R and S are the midpoints of sides AB, BС, CD and DA, respectively, of rectangle ABCD; then quadrilateral PQRS is a ______.

Options

• rectangle

• rhombus

• square

• parallelogram

Answer 1

P, Q, R and S are the midpoints of sides AB, BС, CD and DA, respectively, of rectangle ABCD; then quadrilateral PQRS is a rhombus.

Explanation:

By the Midpoint Theorem, the sides of the quadrilateral formed by joining the midpoints of a rectangle are parallel and equal to half the length of the rectangle’s diagonals. Since the diagonals of a rectangle are equal in length, all four sides of the inner quadrilateral PQRS are equal, making it a rhombus.