Lines and Angles Class 9 Important Questions Free PDF Download

Lines and angles form the foundation of geometry, making Chapter 6 an essential topic for Class 9 CBSE Mathematics. Mastering this chapter not only enhances your conceptual understanding but also helps you solve practical geometry problems effectively. The chapter delves into the basics of lines, angles, their types, and relationships, such as complementary, supplementary, adjacent angles, and vertically opposite angles. It also covers properties of intersecting and parallel lines, along with the angles formed by a transversal. 

Additionally, the angle sum property of a triangle is a crucial concept frequently tested in exams. To ensure a solid grasp of these topics, practising important questions is key. These class 9 lines and angles important questions are designed to test your knowledge, application skills, and problem-solving abilities, making them a vital part of your exam preparation. Let’s explore some essential questions to help you excel in this chapter with confidence!

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Chapter 6 Lines and Angles Important Questions

The figure below consists of a square and an equilateral triangle connected together with a common side

In the design, DF and IG are two iron rods perpendicular to BC. The measure of ∠BAC = 120°.

1. Which type of triangle is ABC? Why?

Solutions: 

To determine the type of triangle △ABC, let us analyze the given information:

△ABC is a triangle with ∠BAC=120°

The triangle contains angles ∠ABC and ∠ACB, with their sum equal to 60°(since the sum of angles in a triangle is 180°).

Type of Triangle

Since one angle in △ABC is greater than 90°, △ABC is an obtuse-angled triangle.

Reasoning

A triangle is classified as obtuse if one of its interior angles measures more than 90°. Here, ∠BAC=120° which satisfies this condition.

2. The central triangle AFG is equilateral. What is the measure of ∠FDA?

Solutions:

Given:

△AFG is equilateral, meaning all its angles measure 60°, including∠FAG,∠AFG, and ∠GAF.

DF is perpendicular to BC, so ∠FDA=90°

To find:

The measure of ∠FDA.

Solution:

Since DF is perpendicular to BC, we know:

∠FDA=90°

3. The length of IG is half of the length of GC. Write a proof for the statement.

Solutions:

Given:

IG is perpendicular to BCBCBC

△AFG is equilateral.

DF and IG are perpendicular to BC.

BC is divided into three equal parts: BF, FG, and GC  because △ABC is symmetrically constructed around the equilateral triangle △AFG

To find:

IG= ½ GC

Solution:

Division of BC:

Since △AFG is equilateral and symmetrically situated in △ABC, the base BC is divided into three equal parts:

BF=FG=GC

Let BF=FG=GC=x. Then the total length of BC=3x

The height of an equilateral triangle is given by:

Height= √3/2 ×side

Since AFG is equilateral with side FG=x, the height h_A of △AFG is:

h_A​= √3/2 ×x

Height IG in △AGC:

IG is the height of △AGC where GC=x and AG is the median of △ABC from vertex A to side BC

△AGC is an isosceles triangle (because AFG is equilateral and symmetric), and the height IG splits △AGC into two smaller congruent right triangles.

Relation between IG and GC

The height IG of △AGC is exactly half the height of △AFG, due to the symmetry of the equilateral triangle and the proportional division of BC

Therefore: 

IG= ½ GC

Chapter 6 Lines and Angles Important Concepts

This chapter helps you understand the basic concepts of geometry related to lines and angles. Here's a simple summary of the important topics covered:

Basic Terms and Definitions:

A line extends infinitely in both directions and has no endpoints.

A line segment has two endpoints.

A ray starts from one point and extends infinitely in one direction.

An angle is formed when two rays meet at a common point, called the vertex.

Types of Angles:

Acute Angle: Less than 90°.

Right Angle: Exactly 90°.

Obtuse Angle: Between 90° and 180°.

Straight Angle: Exactly 180°.

Reflex Angle: Between 180° and 360°.

Pairs of Angles:

Complementary Angles: Two angles whose sum is 90°.

Supplementary Angles: Two angles whose sum is 180°.

Adjacent Angles: Two angles that have a common vertex and a common arm but do not overlap.

Linear Pair: Two adjacent angles whose non-common arms form a straight line (sum = 180°).

Vertically Opposite Angles: Formed when two lines intersect; they are always equal.

Properties of Intersecting Lines:

When two lines intersect, the vertically opposite angles are always equal.

The sum of angles around a point is 360°.

Parallel Lines and Transversal:

Parallel Lines: Lines that never meet and are always equidistant.

Transversal: A line that intersects two or more lines at different points.

Angles formed by a transversal:

• Corresponding Angles: Equal in measure.
• Alternate Interior Angles: Equal in measure.
• Alternate Exterior Angles: Equal in measure.
• Co-Interior Angles: Their sum is 180°.

Angle Sum Property of a Triangle:

The sum of the three interior angles of a triangle is always 180°.

By understanding these concepts, you’ll be able to solve problems involving angles, parallel lines, and triangles. Practice the examples and exercises from your textbook to strengthen your understanding!

Chapter 6 Lines and Angles Important Questions: Why

Practicing important questions from Chapter 6: Lines and Angles is crucial for several reasons:

Builds Strong Fundamentals: This chapter forms the base for advanced geometric concepts in higher classes. Practising questions helps you master the basics of lines, angles, and their relationships.

Enhances Problem-Solving Skills: Geometry involves logical thinking and analytical skills. Solving a variety of questions improves your ability to approach problems from different angles.

Improves Exam Readiness: Important questions often cover frequently tested topics and exam-oriented problems. Practising these ensures you are well-prepared for your exams.

Boosts Confidence: Regular practice of key questions strengthens your understanding, enabling you to attempt challenging problems with ease.

Application of Concepts: Working on different types of problems helps you apply theoretical concepts to practical scenarios, making learning more effective.

Start solving these questions to excel in your exams and beyond!

Chapter 6 Lines and Angles Important Questions: How

To effectively prepare for important questions from Chapter 6, follow these steps:

Understand the Basics: Start by thoroughly reading the chapter from your NCERT textbook. Focus on key concepts like types of angles, pairs of angles, properties of intersecting and parallel lines, and the angle sum property of triangles.

Refer to Examples: Go through solved examples in the textbook. These examples illustrate the step-by-step approach to solving different types of questions.

Practice NCERT Questions: Solve all the exercise questions from the NCERT book. These questions form the foundation for most exam patterns.

Focus on Diagrams: Geometry often involves drawing and analyzing diagrams. Practice creating accurate diagrams to visualize and solve problems.

Solve Important Questions: Refer to important question banks, previous year papers, and mock tests. These questions help you identify recurring patterns and exam-oriented topics.

Revise Regularly: Revisit key formulas, theorems, and properties frequently to retain them.

Clear Doubts: Seek help from teachers or peers if you find any concept difficult. Clarity is essential for solving geometry problems.

By following these steps, you'll build confidence and excel in this chapter!

We hope that you practise the above Lines and Angles Class 9 Important Questions and achieve your dream marks.

All the Best!