Important Questions CBSE Class 9 Maths Chapter 8 Quadrilaterals

Understanding quadrilaterals is a key part of Class 9 Mathematics, as this chapter builds the foundation for several advanced geometry concepts. To prepare effectively, it is highly recommended that students practice a wide range of important questions on quadrilaterals for Class 9.

These resources may include extra questions, worksheets, PDFs, and MCQs designed around quadrilaterals. By solving these, students not only revise thoroughly but also sharpen their problem-solving speed and accuracy.

Through consistent practice, learners can master essential topics such as types of quadrilaterals, their properties, related theorems, and real-world applications. All the questions are based on NCERT Solutions for Class 9 Maths Chapter 8 (Quadrilaterals) and strictly follow the CBSE Class 9 Maths syllabus, ensuring complete exam readiness.

For structured preparation, students can also explore platforms like Infinity Learn, which offers comprehensive study materials, worksheets, and guided resources tailored to Class 9 learners.

Key Concepts in Quadrilaterals

Before diving into the questions, ensure you understand these fundamental concepts:

• Types of quadrilaterals: parallelograms, rectangles, squares, rhombuses, and trapeziums.
• Properties of quadrilaterals, such as opposite sides, angles, and diagonals.
• Important theorems like the Midpoint Theorem and their applications.

Quadrilateral Class 9 Extra Questions: Very Short Answer Type Questions

Question: What is a quadrilateral?

Solution: A quadrilateral is a polygon with four sides and four angles.

Question: Name a quadrilateral whose diagonals are equal and bisect each other at right angles.

Solution: Square.

Question: If one angle of a parallelogram is 70°, what are the measures of the other three angles?

Solution: The opposite angle is also 70°, and the adjacent angles are 110° each (since adjacent angles in a parallelogram are supplementary).

Question: In a rhombus, if one angle is 60°, what are the measures of the other three angles?

Solution: The opposite angle is also 60°, and the adjacent angles are 120° each.

Question: True or False: All rectangles are squares.

Solution: False. While all squares are rectangles (having equal angles and opposite sides equal), not all rectangles are squares (since squares require all four sides to be equal).

Question: What is the sum of the interior angles of a quadrilateral?

Solution: 360°.

Question: In a parallelogram, if one angle is twice its adjacent angle, find the measures of all angles.

Solution: Let the smaller angle be x. Then, the adjacent angle is 2x. Since adjacent angles are supplementary: x + 2x = 180° ⇒ 3x = 180° ⇒ x = 60°. Thus, the angles are 60°, 120°, 60°, and 120°.

Question: Name a quadrilateral whose diagonals bisect each other but are not equal.

Solution: Parallelogram.

Question: True or False: The diagonals of a rhombus are equal.

Solution: False. The diagonals of a rhombus bisect each other at right angles but are not necessarily equal.

Question: If the diagonals of a quadrilateral bisect each other at right angles, what type of quadrilateral is it?

Solution: Rhombus.

More Resources for Class 9 NCERT

• NCERT Solutions for Class 9 Science
• NCERT Solutions for Class 9 Social Science
• NCERT Solutions for Class 9 English

1. If the diagonals of a quadrilateral bisect each other, what type of quadrilateral is it?

Solution: A parallelogram is a quadrilateral whose diagonals bisect each other.

2. In a parallelogram, one angle is 75°. Find the other three angles.

Solution: In a parallelogram, opposite angles are equal, and adjacent angles are supplementary.

Given: One angle = 75°

• Opposite angle = 75°
• Adjacent angles = 180° – 75° = 105°Thus, the angles are 75°, 105°, 75°, and 105°.

3. Prove that the sum of all angles in a quadrilateral is 360°.

Solution: A quadrilateral can be divided into two triangles, and the sum of interior angles of a triangle is 180°.

Since there are two triangles, the total sum of the angles is:

180°+180°=360°

180°+180°=360°

Thus, the sum of all angles in a quadrilateral is 360°.

4. If the diagonals of a rhombus are 12 cm and 16 cm, find its side length.

Solution: In a rhombus, the diagonals bisect each other perpendicularly.

Each half-diagonal measures:

122=6cm,162=8cm

212=6 cm,216=8 cm

Using Pythagoras’ theorem:

Side² =62+82

Side² =62+82

Side² =36+64=100

Side² =36+64=100

Side = √100=10cm

Side =100=10 cm

Thus, each side of the rhombus is 10 cm.

5. In a rectangle, one diagonal is inclined to a side at 30°. Find the acute angle between the diagonals.

Solution: In a rectangle, the diagonals bisect each other and are equal in length.

Given: One diagonal makes 30° with a side.

Since diagonals form congruent triangles, the acute angle between the diagonals is:

2×30°=60°

Thus, the acute angle between the diagonals is 60°.

6. A quadrilateral has three angles as 90°, 70°, and 85°. Find the fourth angle.

Solution: Sum of all angles in a quadrilateral = 360°.

Let the fourth angle be x.

90°+70°+85°+x=360°

90°+70°+85°+x=360°

x=360°−(90°+70°+85°)

x=360°−(90°+70°+85°)

x=360°−245°=115°

x=360°−245°=115°

Thus, the fourth angle is 115°.

7. A parallelogram has one angle as three times its adjacent angle. Find all angles.

Solution: Let one angle be x. Then, the adjacent angle is 3x.

Since adjacent angles in a parallelogram are supplementary:

x+3x=180°

x+3x=180°

4x=180°

4x=180°

x=45°

x=45°

Thus, the angles are 45°, 135°, 45°, and 135°.

8. The angles of a quadrilateral are in the ratio 2:3:4:5. Find the measure of each angle.

Solution: Let the angles be 2x, 3x, 4x, and 5x.

Since the sum of all angles in a quadrilateral is 360°:

2x+3x+4x+5x=360°

14x=360°

x=25°

Thus, the angles are:

2x=50°,3x=75°,4x=100°,5x=125°

9. Prove that the diagonals of a rectangle are equal.

Solution: Let ABCD be a rectangle with diagonals AC and BD.

We prove AC = BD using congruence of triangles.

In ΔABC and ΔBAD:

• AB = AD (opposite sides of a rectangle are equal).
• BC = CD (opposite sides of a rectangle are equal).
• ∠ABC = ∠BAD = 90° (rectangle has right angles).Thus, by SAS Congruence,

△ABC≅△BAD

△ABC≅△BAD

So, AC = BD (corresponding parts of congruent triangles are equal).

Hence, the diagonals of a rectangle are equal.

10. If one diagonal of a parallelogram bisects one of its angles, show that it is a rhombus.

Solution: Let ABCD be a parallelogram where diagonal AC bisects ∠A.

Since diagonal bisects the angle, we get:

∠1=∠2

∠1=∠2

In ΔABC and ΔADC:

• AB = AD (opposite sides of parallelogram).
• AC = AC (common side).
• ∠1 = ∠2 (given).Thus, ΔABC ≅ ΔADC (SAS congruence).So, BC = CD (corresponding parts of congruent triangles).Since all sides are equal, ABCD is a rhombus.

Quadrilateral Class 9 Extra Questions

1. Define a quadrilateral. List six types of quadrilaterals.

Solution:

A quadrilateral is a polygon with four sides (edges) and four vertices (corners).

Six types of quadrilaterals are:

1. Parallelogram
2. Rectangle
3. Square
4. Rhombus
5. Trapezium (or Trapezoid)
6. Kite

2. In which quadrilateral are the diagonals equal and bisect each other at right angles?

Solution:

In a square, the diagonals are equal in length and bisect each other at right angles (90°).

3. Identify the type of quadrilateral formed by joining the midpoints of consecutive sides of a quadrilateral whose diagonals are:

a) Perpendicular

b) Equal

Solution:

a) If the diagonals of a quadrilateral are perpendicular, joining the midpoints of its consecutive sides forms a rectangle.

b) If the diagonals of a quadrilateral are equal, joining the midpoints of its consecutive sides forms a rhombus.

4. In a parallelogram, if one angle measures 80°, find all the angles.

Solution:

In a parallelogram, opposite angles are equal, and adjacent angles are supplementary (sum to 180°).

Given one angle = 80°.

Therefore, the opposite angle is also 80°.

The adjacent angles = 180° – 80° = 100°.

Thus, the angles are 80°, 100°, 80°, and 100°.

5. In a rectangle, one diagonal is inclined to one of its sides at 25°. Determine the acute angle between the two diagonals.

Solution:

In a rectangle, diagonals are equal and bisect each other.

Given: One diagonal makes a 25° angle with a side.

Since diagonals bisect each other, they form two congruent triangles.

The acute angle between the diagonals = 2 × 25° = 50°.

6. Is it possible to have a quadrilateral with all angles obtuse? Explain.

Solution:

No, it’s not possible.

The sum of all interior angles of a quadrilateral is 360°.

An obtuse angle is greater than 90°.

If all four angles were obtuse, their sum would exceed 360°, which contradicts the angle sum property of quadrilaterals.

7. Prove that the angle bisectors of a parallelogram form a rectangle.

Solution:

In a parallelogram, adjacent angles are supplementary.

The bisectors of adjacent angles intersect to form angles of 90°.

Thus, the quadrilateral formed by the angle bisectors is a rectangle.

8. In a trapezium, the angles adjacent to the non-parallel sides are 55° and 70°. Find the other two angles.

Solution:

In a trapezium, the sum of angles adjacent to each non-parallel side is 180°.

Let the trapezium be ABCD with AB || CD.

Given: ∠A = 55°, ∠B = 70°.

∠D = 180° – ∠A = 180° – 55° = 125°.

∠C = 180° – ∠B = 180° – 70° = 110°.

Thus, the angles are 55°, 70°, 125°, and 110°.

9. Calculate all the angles of a parallelogram if one of its angles is twice its adjacent angle.

Solution:

Let one angle be x.

Its adjacent angle = 2x.

Since adjacent angles in a parallelogram are supplementary:

x + 2x = 180°

3x = 180°

x = 60°

Therefore, the angles are 60°, 120°, 60°, and 120°.

10. The angles of a quadrilateral are in the ratio 2:5:4:1. Find the measure of each angle.

Solution:

Let the common ratio be x.

Then, the angles are 2x, 5x, 4x, and 1x.

Sum of angles in a quadrilateral = 360°

2x + 5x + 4x + x = 360°

12x = 360°

x = 30°

Therefore, the angles are:

2x = 60°

5x = 150°

4x = 120°

1x = 30°