Important Questions for Class 9 Maths (Ganita Manjari II) Chapter 12 Quadrilaterals 2026-27

The important questions for Class 9 Maths Chapter 12 help students apply the properties of quadrilaterals to solve problems involving angles, sides and diagonals. Practise the questions below to strengthen your geometrical reasoning, understand each solution and improve accuracy in school exams.

Class 9 Maths Chapter 12 Important Questions – MCQs

Q1. A quadrilateral has three interior angles measuring 75°, 95° and 110°. What is the fourth angle?

A) 70°

B) 80°

C) 90°

D) 100°

Answer: B) 80°

Solution:

Sum of interior angles of a quadrilateral = 360°

Fourth angle = 360° − (75° + 95° + 110°)

= 360° − 280°

= 80°

Q2. Which of the following conditions is sufficient to prove that a quadrilateral is a parallelogram?

A) Only one pair of opposite sides is equal

B) Its diagonals have equal lengths

C) Its diagonals bisect each other

D) Two adjacent sides are equal

Answer: C) Its diagonals bisect each other.

Explanation: According to the converse of the diagonal property of parallelograms, a quadrilateral whose diagonals bisect each other is a parallelogram.

Q3. In triangle ABC, P and Q are the midpoints of AB and AC respectively. If BC = 18 cm, what is the length of PQ?

A) 6 cm

B) 9 cm

C) 12 cm

D) 18 cm

Answer: B) 9 cm

Q4. Which statement is always true about the centroid of a triangle?

A) It divides each median into two equal parts.

B) It divides each median in the ratio 2 : 1 from the vertex.

C) It lies at the midpoint of the longest side.

D) It is the intersection of the perpendicular bisectors.

Answer: B) It divides each median in the ratio 2 : 1 from the vertex.

Explanation: The three medians of a triangle meet at the centroid. The centroid divides each median into two parts in the ratio 2 : 1, with the longer part towards the vertex.

Class 9 Maths Chapter 12 Very Short Answer Questions

Q5. What is the difference between a convex and a non-convex quadrilateral?

Answer:

A convex quadrilateral has all its interior angles less than 180°.

A non-convex quadrilateral has at least one interior angle greater than 180°, forming an inward dent.

Q6. The diagonals of parallelogram ABCD intersect at O. If AC = 16 cm and BD = 22 cm, find AO and BO.

Answer:

AO = 8 cm and BO = 11 cm, because the diagonals bisect each other.

Q7. G is the centroid of triangle ABC, and AD is a median. If AG = 10 cm, find GD.

Answer: 

AG : GD = 2 : 1. Therefore, GD = 5 cm.

Class 9 Maths Chapter 12 Short Answer Questions

Q8. The adjacent angles of a parallelogram are (3x + 10)° and (2x − 5)°. Find all its angles.

Solution:

Adjacent angles of a parallelogram add up to 180°.

(3x + 10) + (2x − 5) = 180

5x + 5 = 180

x = 35

Therefore:

3x + 10 = 115°

2x − 5 = 65°

Opposite angles are equal.

Answer: The angles are 115°, 65°, 115° and 65°.

Q9. In parallelogram ABCD, AB = 3x + 2 cm and CD = 5x − 8 cm. If BC = 9 cm, find its perimeter.

Solution:

Opposite sides of a parallelogram are equal.

3x + 2 = 5x − 8

2x = 10

x = 5

AB = 3 × 5 + 2 = 17 cm.

Perimeter = 2 × (AB + BC)

= 2 × (17 + 9)

= 52 cm.

Answer: 52 cm.

Q10. In triangle ABC, P and Q are the midpoints of AB and AC. If PQ = x + 3 cm and BC = 4x − 2 cm, find x and BC.

Solution:

By the Midpoint Theorem, BC = 2PQ.

4x − 2 = 2(x + 3)

4x − 2 = 2x + 6

x = 4

Therefore, BC = 4 × 4 − 2 = 14 cm.

Answer: x = 4 and BC = 14 cm.

Q11. In triangle ABC, D is the midpoint of AB. A line through D parallel to BC meets AC at E. If AC = 18 cm and BC = 14 cm, find AE, EC and DE.

Solution:

By the converse of the Midpoint Theorem, E is the midpoint of AC.

AE = EC = 18 ÷ 2 = 9 cm.

Since D and E are midpoints, the Midpoint Theorem gives:

DE = 14 ÷ 2 = 7 cm.

Answer: AE = 9 cm, EC = 9 cm and DE = 7 cm.

Class 9 Maths Chapter 12 Long Answer Questions

Q12. Prove that a quadrilateral whose opposite sides are equal is a parallelogram.

Given: In quadrilateral ABCD, AB = CD and BC = AD.

To prove: ABCD is a parallelogram.

Construction: Draw diagonal AC.

Proof:

In triangles ABC and CDA:

- AB = CD — given.

- BC = DA — given.

- AC = CA — common side.

Therefore, △ABC ≅ △CDA by SSS congruence.

Corresponding angles are equal:

∠BAC = ∠DCA

∠BCA = ∠DAC

The first pair gives AB ∥ CD by the converse of the alternate interior angles property.

The second pair gives BC ∥ AD.

Both pairs of opposite sides are parallel.

Hence, ABCD is a parallelogram.

Q13. Prove that a quadrilateral whose diagonals bisect each other is a parallelogram.

Given: Diagonals AC and BD of quadrilateral ABCD intersect at O, with AO = OC and BO = OD.

To prove: ABCD is a parallelogram.

Proof:

In triangles AOB and COD:

- AO = CO — given.

- BO = DO — given.

- ∠AOB = ∠COD — vertically opposite angles.

Therefore, △AOB ≅ △COD by SAS congruence.

Thus, ∠BAO = ∠DCO.

These are alternate interior angles with transversal AC. Hence, AB ∥ CD.

Similarly, in triangles AOD and COB:

- AO = CO.

- DO = BO.

- ∠AOD = ∠COB — vertically opposite angles.

Therefore, △AOD ≅ △COB by SAS congruence.

Thus, ∠DAO = ∠BCO, giving AD ∥ BC.

Hence, ABCD is a parallelogram.

Tips to Solve Class 9 Maths Chapter 12 Quadrilaterals Questions

Understanding quadrilateral properties helps students solve geometry problems accurately. Keep these points in mind while practising:

• Identify the Quadrilateral: Check its sides, angles and diagonals before applying a property.

• Remember Angle Rules: The sum of interior angles of a quadrilateral is 360°.

• Use Diagonal Properties: Understand how diagonals differ in parallelograms, rectangles and rhombuses.

• Draw Clear Figures: Mark known angles and measurements to avoid confusion.

• Explain Your Steps: Give valid mathematical reasons when solving proofs.

Benefits of Vedantu's Class 9 Maths Chapter 12 Important Questions PDF

Vedantu's Class 9 Maths Chapter 12 Important Questions with Solutions provides focused practice for Quadrilaterals in Ganita Manjari Part II.

• Solved Questions: Understand the correct methods through clear explanations.

• MCQ Practice: Test your understanding with Class 9 Maths Chapter 12 Important Questions MCQs.

• Self-Assessment: Check answers and identify areas that need improvement.

• PDF Download: Save the questions for convenient offline practice.

Use Vedantu's Class 9 Maths Chapter 12 Important Questions PDF to prepare for the 2026-27 school exams.

Important Study Materials for Class 9 Maths (Ganita Manjari  II) Chapter 12 Quadrilaterals

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