Free printable worksheet
Class 9 · Mathematics · 10 Aug 2026
Identify the quadrilateral whose diagonals are perpendicular to each other but are NOT necessarily of equal length.
[1 mark]Identify the quadrilateral formed by joining the midpoints of the sides of a quadrilateral taken in order, if the diagonals of the original quadrilateral are perpendicular.
[1 mark]Match each special quadrilateral with its defining diagonal property.
[2 marks]| Column A | Column B |
|---|---|
| 1. Rhombus | a. Diagonals bisect each other at right angles |
| 2. Rectangle | b. Diagonals are equal in length and bisect each other |
| 3. Square | c. Diagonals are equal and bisect at right angles |
| 4. Parallelogram | d. Diagonals bisect each other but not at right angles |
Answer: __________________________________________
Match each special quadrilateral with its unique diagonal property.
[2 marks]| Column A | Column B |
|---|---|
| 1. Rhombus | a. Diagonals bisect at right angles |
| 2. Rectangle | b. Diagonals are equal in length |
| 3. Kite | c. Diagonals intersect at right angles, one bisects the other |
| 4. Square | d. Diagonals are equal and bisect at right angles |
Answer: __________________________________________
The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and is _____ of the third side.
[1 mark]Define a rhombus in terms of its sides and diagonals.
[1 mark]Diagonals of a quadrilateral ABCD intersect each other at point O such that AO/BO = CO/DO. Show that ABCD is a trapezium.
[4 marks]In a geometry lab at a school in Jaipur, Priya constructs a quadrilateral ABCD by joining the midpoints of the consecutive sides of a given quadrilateral PQRS. Prove that the quadrilateral ABCD is a parallelogram, stating the relevant theorem used.
[3 marks]Rohan is designing a decorative garden boundary in his courtyard in Jaipur shaped like a quadrilateral PQRS. He measures the sides and finds that PQ = SR = 7 m and PS = QR = 7 m, but the diagonal PR is 10 m and diagonal QS is 7 m. Classify the quadrilateral PQRS precisely based on these measurements and justify why it cannot be a square.
[3 marks]Identify the labeled components in the given parallelogram ABCD with diagonals AC and BD intersecting at O.
[2 marks]