1. Sum of the angles of any quadrilateral is ____ degrees.
- A180
- B270
- C360
- D540
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Answer: C) 360
Quadrilateral splits into 2 triangles; each contributes 180°. 2 × 180 = 360°.
Class 9 Quadrilaterals — practice questions with answers
Geometry — Quadrilaterals · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. How many diagonals does a quadrilateral have?
- A1
- B3
- C4
- D2
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Answer: D) 2
A quadrilateral has 4 vertices. Number of diagonals = n(n-3)/2 = 4(1)/2 = 2. They join the two pairs of non-adjacent vertices.
3. Which quadrilateral has all sides equal but angles that need NOT be 90°?
- ARectangle
- BSquare
- CRhombus
- DTrapezium
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Answer: C) Rhombus
A rhombus has all four sides equal but its angles need not be right angles. A square has all sides equal AND all angles 90°.
4. Which of the following quadrilaterals does NOT always have diagonals that bisect each other?
- AParallelogram
- BRectangle
- CTrapezium
- DRhombus
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Answer: C) Trapezium
Diagonals bisect each other in all parallelograms (including rectangles and rhombuses). A general trapezium is not a parallelogram, so its diagonals do not bisect each other.
5. ABCD is a parallelogram and P, Q are midpoints of sides AB and DC respectively. What can you conclude about quadrilateral APQD?
- AAPQD is necessarily a parallelogram
- BAPQD is necessarily a rectangle
- CAPQD is a trapezium but not a parallelogram
- DNo definite conclusion can be drawn about APQD
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Answer: A) APQD is necessarily a parallelogram
AB ∥ DC and AB = DC. Their halves AP and DQ are therefore equal and parallel. One pair of opposite sides equal and parallel makes APQD a parallelogram, so the answer is Yes.
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