How many practice questions are available for Quadrilaterals?

SparkEd Math offers 60+ practice questions for Quadrilaterals across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Quadrilaterals content free on SparkEd Math?

Yes! All Quadrilaterals content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Quadrilaterals differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Quadrilaterals problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Quadrilaterals content aligned with the CBSE syllabus?

Yes, all Quadrilaterals questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Quadrilaterals — Class 9 CBSE (2025-26)

About Quadrilaterals — Class 9 CBSE

Prove angle sum property, properties of parallelograms, and mid-point theorem. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 8). On this page you can practice 65 questions across three difficulty levels — 20 easy, 21 medium, and 24 hard — each with a visual step-by-step solution, plus a timed 40-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Quadrilaterals

Introduction to Quadrilaterals: The Four-Sided Wonders
Unlocking Parallelograms: Properties and Proofs
Mid-point Theorem and Proving Parallelograms
Special Quadrilaterals: Rectangles, Rhombuses, and Squares
Putting it All Together: Applications and NCERT Practice

Interactive lesson · about 15 minutes · checkpoint question after every unit

Quadrilaterals — solved examples for Class 9 CBSE

Example 1easy

Which of the following statements about the angle sum property of a quadrilateral is TRUE?

A)The sum of interior angles of any quadrilateral is 180°.
B)The sum of interior angles of a convex quadrilateral is 360°.
C)The sum of interior angles of a concave quadrilateral is less than 360°.
D)The sum of interior angles of a quadrilateral can vary depending on its type.

Step-by-step solution

Any quadrilateral, whether convex or concave, can be divided into two triangles by drawing one of its diagonals.
Since the sum of angles in each triangle is 180°, the sum of angles in the quadrilateral will be 2 × 180° = 360°.
This property holds true for all quadrilaterals, convex or concave.

Answer: The sum of interior angles of a convex quadrilateral is 360°.

Example 2medium

In a quadrilateral ABCD, the angles are in the ratio 3:5:9:13. Find the measure of the largest angle.

A)39°
B)117°
C)156°
D)130°

Step-by-step solution

Let the angles of the quadrilateral be 3x, 5x, 9x, and 13x.
The sum of the interior angles of a quadrilateral is 360°.
$3x + 5x + 9x + 13x = 360°$
Combine the terms: 30x = 360°. Solve for x: x = 360° / 30 = 12°.
The largest angle is 13x. So, 13 × 12° = 156°.

Answer: 156°

Example 3hard

In a quadrilateral ABCD, the bisectors of ∠A and ∠B meet at P. If ∠C = 100° and ∠D = 80°, what is the measure of ∠APB?

A)80°
B)90°
C)100°
D)110°

Step-by-step solution

The sum of angles in a quadrilateral ABCD is 360°. So, ∠A + ∠B + ∠C + ∠D = 360°.
Substitute the given values: ∠A + ∠B + 100° + 80° = 360°. This means ∠A + ∠B = 360° - 180° = 180°.
In ΔAPB, ∠PAB = ∠A/2 and ∠PBA = ∠B/2 (since AP and BP are angle bisectors). The sum of angles in ΔAPB is 180°.
So, ∠APB + ∠A/2 + ∠B/2 = 180° => ∠APB + (∠A + ∠B)/2 = 180°. Substituting ∠A + ∠B = 180°, we get ∠APB + 180°/2 = 180° => ∠APB + 90° = 180° => ∠APB = 90°.

Answer: 90°

Practice questions on Quadrilaterals

Q1.easy
Ravi was given a quadrilateral ABCD. He concluded that if AB = CD and BC = DA, then ABCD must be a parallelogram. Is Ravi's reasoning correct?
1. A)Yes, because a quadrilateral with opposite sides equal is always a parallelogram.
2. B)No, because only opposite angles being equal guarantees it's a parallelogram.
3. C)No, because the diagonals must also bisect each other for it to be a parallelogram.
4. D)Yes, but only if all angles are 90°.
Show answer
Answer: Yes, because a quadrilateral with opposite sides equal is always a parallelogram.
Hint: Consider the defining properties of a parallelogram and the conditions that make a quadrilateral a parallelogram.
Q2.easy
Consider a quadrilateral PQRS where the diagonals PR and QS intersect at point O. If PO = OR and QO = OS, which of the following statements is definitely TRUE?
1. A)PQRS is a rhombus.
2. B)PQRS is a rectangle.
3. C)PQRS is a parallelogram.
4. D)PQRS is a kite.
Show answer
Answer: PQRS is a parallelogram.
Hint: Think about the unique property of diagonals in a parallelogram.
Q3.easy
In a parallelogram ABCD, ∠A = 70°. What are the measures of ∠B, ∠C, and ∠D respectively?
1. A)∠B = 70°, ∠C = 110°, ∠D = 110°
2. B)∠B = 110°, ∠C = 70°, ∠D = 110°
3. C)∠B = 110°, ∠C = 110°, ∠D = 70°
4. D)∠B = 70°, ∠C = 70°, ∠D = 110°
Show answer
Answer: ∠B = 110°, ∠C = 70°, ∠D = 110°
Hint: Remember the properties of opposite angles and consecutive angles in a parallelogram.
Q4.medium
ABCD is a parallelogram. If ∠A = (3x - 5)° and ∠C = (2x + 25)°, find the measure of ∠B.
1. A)30°
2. B)35°
3. C)145°
4. D)150°
Show answer
Answer: 145°
Hint: Recall the property of opposite angles in a parallelogram. Once you find x, use the property of consecutive angles.
Q5.medium
ABCD is a parallelogram. The diagonals AC and BD intersect at O. If AO = 5 cm and BO = 7 cm, what are the lengths of AC and BD respectively?
1. A)10 cm, 14 cm
2. B)5 cm, 7 cm
3. C)10 cm, 7 cm
4. D)5 cm, 14 cm
Show answer
Answer: 10 cm, 14 cm
Hint: Think about the property of diagonals of a parallelogram regarding their point of intersection.
Q6.medium
Which of the following conditions is NOT sufficient to prove that a quadrilateral is a parallelogram?
1. A)Both pairs of opposite sides are equal.
2. B)Both pairs of opposite angles are equal.
3. C)Diagonals bisect each other.
4. D)One pair of opposite sides is equal.
Show answer
Answer: One pair of opposite sides is equal.
Hint: Consider each condition carefully. For a quadrilateral to be a parallelogram, it needs to satisfy certain specific properties. Think of quadrilaterals that satisfy the incorrect option but are not parallelograms.
Q7.hard
A parallelogram ABCD has its diagonals AC and BD intersecting at O. If AC = (3x - 10) cm and AO = (x + 10) cm, find the length of BD, given that BO = (y + 5) cm and OD = (2y - 15) cm.
1. A)40 cm
2. B)50 cm
3. C)60 cm
4. D)70 cm
Show answer
Answer: 70 cm
Hint: Recall the property of diagonals in a parallelogram. They bisect each other. This means AO = OC and BO = OD.
Q8.hard
A parallelogram ABCD has its diagonals AC and BD intersecting at O. If AC = (3x - 10) cm and AO = (x + 10) cm, find the length of BD, given that BO = (y + 5) cm and OD = (2y - 15) cm.
1. A)40 cm
2. B)50 cm
3. C)60 cm
4. D)70 cm
Show answer
Answer: 70 cm
Hint: Remember that the diagonals of a parallelogram bisect each other. This means AO = OC and BO = OD. Use this to find the values of x and y, then calculate BD.
Q9.hard
In parallelogram ABCD, P is the midpoint of AB and Q is the midpoint of CD. If diagonal AC intersects PQ at R, and the area of ΔARC is 15 cm², what is the area of parallelogram ABCD?
1. A)60 cm²
2. B)90 cm²
3. C)120 cm²
4. D)180 cm²
Show answer
Answer: 120 cm²
Hint: Consider the line segment PQ. What type of figure is APCQ? How does the line PQ relate to AC? Think about medians and triangle areas.

These are 9 of the 65 questions available for Quadrilaterals. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.