Quadrilaterals Class 9 Important Questions Free PDF Download

Quadrilaterals are one of the most fundamental topics in Class 9 Mathematics. This chapter lays the foundation for understanding two-dimensional shapes and their properties, which are crucial for solving a variety of geometric problems. To excel in your exams, practising important questions on this topic is essential.

In this blog, we’ll provide a collection of important questions of Quadrilaterals Class 9 that cover key concepts like types of quadrilaterals, theorems, and their applications. These questions are designed to help you gain clarity and confidence while preparing for your CBSE exams. Whether it’s understanding the properties of parallelograms or applying the Midpoint Theorem, these questions will guide you step-by-step.

So, dive in and start practising to strengthen your grip on this important chapter!

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Important Question: Quadrilateral Class 9

In the quadrilateral ABCD given below, ∠DAC = 90° and AB = AC = AD = DE = EB.

1. What is the value of ∠EAC?

a. 15°

b. 30°

c. 45°

d. 90°

Solution: 

(a) 15°

Explanations:

Since AB=AC=AD, △DAC is an isosceles right triangle (∠ACD=∠ADC=45°)

DE and EB are equal, forming an equilateral triangle at △DEB, with all angles 60°

∠DAB=30° (given).

∠DAC=90° (given)

∠EAC=∠DAB−∠EAD

∠EAD is half of ∠DAB (as DE=AD)

∠EAD = 30°/2

∠EAD = 15°

Therefore, ∠EAC=30°−15°

=15°

2. Which type of quadrilateral is ABCE?

a. Rhombus

b. Kite 

c. Trapezium

d. Parallelogram

Solution:

(b) kite

Explanations:

AB=AC=EB=DE

Quadrilateral ABCE has two pairs of adjacent sides equal, making it a kite (properties of a kite).

Hence, the given figure is a kite

3. What is the value of ∠ABE?

a. 20°

b. 30° 

c. 45°

d. 60°

Solution:

(d) 60°

Explanations:

△ABE is isosceles (AB=EB)
In △DEB, ∠DEB=60° and it splits evenly as ∠DEA=∠AEB=30° (since DE=EB).

∠ABE=90°−∠AEB (exterior angle property in △ABE)

∠ABE=90°−30°

=60°

4. The area of a triangle and a parallelogram are equal. Which of the following statements is true for them?

a. The base length and the altitude of the triangle and the parallelogram are the same.

b. Both the triangle and the parallelogram lie between the same set of parallel lines and their bases are the same.

c. The base length and the corresponding altitude of the triangle are two times the base length and the corresponding altitude of the parallelogram.

d. Either the corresponding base length or the corresponding altitude of the triangle is double the parallelogram’s base length or altitude. 

Solution:

(d) Either the corresponding base length or the corresponding altitude of the triangle is double the parallelogram’s base length or altitude. 

Explanations:

Area of a triangle = ½ ×base×altitude

Area of a parallelogram = base×altitude

The areas of the triangle and parallelogram are equal:

½ ×base×altitude = base×altitude

b_t​×h_t​=2×b_p​×h_p​

This means that either the base or the altitude of the triangle must be double the corresponding dimension of the parallelogram.

In the figure given below, each small square represents an area of 1 cm². 

5. What is the ratio between the area of the square and the shaded region?

a. 1:1

b. 25:6

c. 3:1

d. 3:2

Solution: 

(b) 25:6

Explanations:

Area of the square = 25 cm²

Area of the shaded region ABCD = 6 cm²

Ratio = Square Area/Shaded Area

Ratio = 25 cm²/6 cm²

Ratio = 25/6

Ratio = 25:6

6. What is the area (in cm²) of the trapezium in the given figure?

a. 6 cm²

b. 8 cm²

c. 9 cm²

d. 12 cm² 

Solution: 

(a) 6 cm²

Explanations:

The two parallel sides are 2 cm and 4 cm.

The height (distance between the parallel sides) is 2 cm.

Area= ½ X (2+4)×2

Area= ½ x 6 x 2

Area= 6 cm²

Important Questions Concepts: Quadrilateral Class 9

A quadrilateral is a four-sided polygon with four vertices and four angles. In this chapter, you learn about the properties, types, and important theorems related to quadrilaterals.

Key Concepts:

Definition: A quadrilateral has:

• Four sides
• Four vertices
• The sum of its interior angles = 360°

Types of Quadrilaterals:

Parallelogram: Opposite sides are parallel and equal; opposite angles are equal.

Rectangle: All angles are 90°; opposite sides are equal and parallel.

Square: All sides are equal; all angles are 90°.

Rhombus: All sides are equal; opposite angles are equal.

Trapezium: Only one pair of opposite sides is parallel.

Kite: Two pairs of adjacent sides are equal.

Important Theorems:

Theorem 1: The diagonal of a parallelogram divides it into two congruent triangles.

Theorem 2: In a parallelogram:

1. Opposite sides are equal.
2. Opposite angles are equal.
3. Diagonals bisect each other.

Theorem 3: A quadrilateral is a parallelogram if:

1. Both pairs of opposite sides are equal.
2. Both pairs of opposite angles are equal.
3. Diagonals bisect each other.

Midpoint Theorem: The line segment joining the midpoints of two sides of a triangle is parallel to the third side and half of its length.

Applications:

• Understanding quadrilaterals helps solve geometry problems related to shapes, area, and dimensions.
• It is a foundation for advanced geometry topics in higher classes.

This chapter emphasizes understanding the relationships and properties of different quadrilaterals through diagrams, proofs, and examples, which is essential for building logical reasoning in mathematics.

Important Question Quadrilateral Class 9: Why

The chapter on Quadrilaterals in Class 9 is not just about shapes and figures; it’s about building a strong foundation in geometry. Understanding this topic is vital for some reasons:

Core Concepts for Higher Studies: Quadrilaterals form the basis for more advanced topics in geometry, such as coordinate geometry, mensuration, and trigonometry. A clear understanding now will make future learning easier.

Scoring Potential: Questions from this chapter frequently appear in exams. Practising important questions helps you become familiar with commonly asked problems, giving you an edge in scoring well.

Application of Theorems: This chapter focuses on applying key theorems like the Midpoint Theorem, properties of parallelograms, and diagonals of quadrilaterals. These theorems are not only important for exams but also for solving real-world problems.

Boosts Logical Thinking: Solving geometry problems improves logical reasoning and problem-solving skills. By practicing a variety of questions, you develop a methodical approach to tackling complex problems.

CBSE Exam Patterns: Practicing important questions aligned with CBSE exam patterns helps you understand the type of questions, the marking scheme, and the best way to present your answers.

By focusing on these important questions, you’ll strengthen your grasp of the topic, enhance your problem-solving abilities, and be better prepared for both board exams and future studies. Remember, consistent practice is the key to mastering Quadrilaterals! We hope that you practice the above Quadrilateral Class 9 Important Questions and achieve your dream marks.

All the Best!