Quadrilaterals — Class 9 MCQs with Answers
Class 9 CBSE Mathematics · Chapter 13
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 9 CBSE Mathematics questions from Chapter 13, "Quadrilaterals". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE Board exams and the JEE & NEET foundation years apart.
To score well in "Quadrilaterals", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Quadrilaterals, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Quadrilaterals (Class 9 Mathematics)
A quadrilateral's angles always sum to 360°, and the parallelogram family is defined by which sides and diagonals are equal or parallel. This chapter proves the parallelogram properties and their converses, and establishes the mid-point theorem.
- Quadrilateral
- A closed figure with four sides, four vertices and four angles, whose interior angles always add to 360°.
- Angle sum property
- The four interior angles total 360°, proved by splitting the quadrilateral into two triangles with a diagonal.
- Parallelogram
- A quadrilateral with both pairs of opposite sides parallel — the parent shape of the rectangle, rhombus and square.
- Opposite sides and angles
- In a parallelogram opposite sides are equal and opposite angles are equal; each result follows from congruent triangles.
Quadrilaterals — important questions & MCQs with answers (Class 9 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
The sum of interior angles of a quadrilateral is:
A.180°B.270°C.540°D.360°✓ CorrectAnswer: D. 360°
Explanation: A quadrilateral splits into two triangles by one diagonal, so its angles total 2×180° = 360°. A common mistake is applying a triangle's 180° rule directly to a four-sided figure.
- Q2Easy
A quadrilateral in which both pairs of opposite sides are parallel is called a:
A.TrapeziumB.RhombusC.Parallelogram✓ CorrectD.RectangleAnswer: C. Parallelogram
Explanation: A quadrilateral with both pairs of opposite sides parallel is defined as a parallelogram — a trapezium has only one such pair, so it doesn't qualify here.
- Q3Easy
The Mid-Point Theorem states that the segment joining midpoints of two sides of a triangle is:
A.Equal to the third sideB.Parallel to and half of the third side✓ CorrectC.Perpendicular to the third sideD.Double the third sideAnswer: B. Parallel to and half of the third side
Explanation: The Mid-Point Theorem: the segment joining the midpoints of two sides of a triangle is parallel to the third side and exactly half its length — not equal to it or double it.
- Q4Easy
Three angles of a quadrilateral are 70°, 80°, and 110°. Find the fourth angle.
A.90°B.100°✓ CorrectC.110°D.80°Answer: B. 100°
Explanation: The four angles of a quadrilateral sum to 360°, so the fourth angle = 360° − 70° − 80° − 110° = 100°. Forgetting the 360° total (using 180° instead) is the usual slip here.
- Q5Easy
In a parallelogram, opposite sides are:
A.PerpendicularB.Bisecting each otherC.UnequalD.Equal and parallel✓ CorrectAnswer: D. Equal and parallel
Explanation: In a parallelogram, opposite sides are always both equal in length and parallel, proved by splitting it along a diagonal into two congruent triangles (ASA). Don't confuse this with a trapezium, where sides need not be equal.
- Q6Easy
The converse of the Mid-Point Theorem states: A line drawn through the midpoint of one side of a triangle, parallel to another side, bisects:
A.The areaB.The angle at the midpointC.The opposite angleD.The third side✓ CorrectAnswer: D. The third side
Explanation: The converse of the Mid-Point Theorem: a line through one side's midpoint, drawn parallel to a second side, must bisect the third side — this is how midpoints get located without measuring.
- Q7Medium
Angles of a quadrilateral are in ratio 1:2:3:4. Find the largest angle.
A.120°B.144°✓ CorrectC.160°D.100°Answer: B. 144°
Explanation: Let the four angles be x, 2x, 3x, 4x; since they sum to 360°, 10x = 360° gives x = 36°, so the largest angle is 4 × 36° = 144°.
- Q8Medium
In parallelogram ABCD, ∠A=75°. Find all four angles.
A.75°,90°,75°,120°B.75°,75°,75°,75°C.75°,105°,75°,105°✓ CorrectD.60°,120°,60°,120°Answer: C. 75°,105°,75°,105°
Explanation: ∠A and ∠C are opposite angles, so ∠C = ∠A = 75°; ∠B and ∠D are adjacent to ∠A, so each is supplementary: 180° − 75° = 105°. This gives 75°, 105°, 75°, 105° around the shape.
- Q9Medium
In ΔABC, D and E are midpoints of AB and AC. If BC=8cm, find DE.
A.4 cm✓ CorrectB.8 cmC.16 cmD.2 cmAnswer: A. 4 cm
Explanation: By the Mid-Point Theorem, DE (joining the midpoints of AB and AC) equals half of BC: DE = 8/2 = 4 cm. Doubling BC instead of halving it is the usual error.
- Q10Medium
In an isosceles trapezium, each pair of base angles is equal. If one base angle is 65°, find the adjacent angle.
A.115°✓ CorrectB.65°C.130°D.90°Answer: A. 115°
Explanation: In a trapezium, the two angles on the same leg (co-interior angles between the parallel sides) are supplementary, so the adjacent base angle = 180° − 65° = 115°.
- Q11Medium
In parallelogram ABCD, diagonals AC and BD bisect at O. If AO=5cm, find AC.
A.5 cmB.10 cm✓ CorrectC.2.5 cmD.15 cmAnswer: B. 10 cm
Explanation: A parallelogram's diagonals bisect each other, so O is the midpoint of AC, meaning OC = AO = 5 cm and the full diagonal AC = AO + OC = 10 cm.
- Q12Hard
In quadrilateral ABCD, ∠A:∠B:∠C:∠D = 2:3:5:8. Find ∠D.
A.144°B.160°✓ CorrectC.120°D.100°Answer: B. 160°
Explanation: The angles are in ratio 2:3:5:8, summing to 18x = 360°, so x = 20° and ∠D = 8 × 20° = 160°.
- Q13Hard
ABCD is a parallelogram and E is the midpoint of AB. CE produced meets DA produced at F. If AD = 4 cm, find the length of FD.
A.8 cm✓ CorrectB.4 cmC.2 cmD.6 cmAnswer: A. 8 cm
Explanation: In triangles FAE and CBE: AE = EB, the vertically opposite angles at E are equal, and ∠FAE = ∠CBE (alternate angles, AD ∥ BC), so they are congruent and AF = BC = AD = 4 cm. Hence FD = FA + AD = 8 cm.
- Q14Hard
The figure formed by joining the midpoints of a quadrilateral is always a:
A.Parallelogram✓ CorrectB.RectangleC.RhombusD.SquareAnswer: A. Parallelogram
Explanation: Varignon's theorem: joining the midpoints of any quadrilateral's sides in order always produces a parallelogram, whatever the shape of the original quadrilateral — even a non-convex one.
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Start this chapter free →Quadrilaterals — FAQs
What are the key concepts in Class 9 Mathematics Quadrilaterals?+
A quadrilateral's angles always sum to 360°, and the parallelogram family is defined by which sides and diagonals are equal or parallel. This chapter proves the parallelogram properties and their converses, and establishes the mid-point theorem. Key ideas include Quadrilateral, Angle sum property, Parallelogram, Opposite sides and angles.
What does Class 9 Mathematics Chapter 13 (Quadrilaterals) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Quadrilaterals": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Quadrilaterals" questions free to practise?+
Yes. Sign in with Google to practise "Quadrilaterals" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Quadrilaterals" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Quadrilaterals" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Quadrilaterals" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Quadrilaterals (Class 9 Mathematics)?+
The questions that matter most test Quadrilateral, Angle sum property, Parallelogram, Opposite sides and angles. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Quadrilaterals?+
Yes — Class 9 Mathematics Quadrilaterals has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.