Lines and Angles Class 9 Notes

Lines and Angles is a very important chapter in the Class 9 Mathematics syllabus. It helps students to understand the basic shapes, figures, and relationships between different angles formed by lines. The topic will build the base for geometry and is also very useful in higher classes of students also. Below, we will learn about the important concepts, properties, and examples that are related to Lines and Angles.

Basic Concepts of Lines and Angles

A line is a straight path that extends endlessly in both directions. It does not have any endpoints. A ray has one fixed point and extends infinitely in one direction. A line segment has two endpoints and a fixed length. These are the basic building blocks of geometry and are important to understand before learning more about Lines and Angles.

Collinear and Non-Collinear Points

When three or more points lie on the same straight line, they are called collinear points. If the points do not lie on the same line, they are non-collinear points. This concept helps in drawing and identifying figures made using Lines and Angles.

Types of Angles

An angle is formed when two rays meet at a common point called the vertex. There are different types of angles:

• Acute Angle: Less than 90°.
• Right Angle: Exactly 90°.
• Obtuse Angle: More than 90° but less than 180°.
• Straight Angle: Exactly 180°.
• Reflex Angle: Between 180° and 360°.
• Complete Angle: Exactly 360°.

These types help students identify and measure Lines and Angles correctly.

Complementary and Supplementary Angles

When the sum of two angles is 90°, they are called complementary angles. For example, 40° and 50° form complementary angles. When the sum of two angles is 180°, they are supplementary angles. For example, 110° and 70° form supplementary angles. These relations are very common in Lines and Angles questions.

Adjacent Angles and Linear Pair

Two angles that share a common vertex and arm are called adjacent angles. When the non-common arms of adjacent angles form a straight line, they are called a linear pair. The sum of a linear pair is always 180°. These rules are often used to solve Lines and Angles problems.

Vertically Opposite Angles

When two lines cross each other, opposite angles are formed. These are called vertically opposite angles, and they are always equal. This property is a key part of Lines and Angles and helps in finding unknown values in geometry problems.

Parallel Lines and Transversals

When a line cuts two parallel lines, it forms different angle pairs. In Lines and Angles, these are:

• Corresponding Angles: Equal and form an F shape.
• Alternate Interior Angles: Equal and form a Z shape.
• Interior Angles on the Same Side: Add up to 180°.

These properties are very useful for solving questions related to Lines and Angles in triangles and other figures.

Angle Sum Property of Triangle

The sum of all interior angles of a triangle is always 180°. The exterior angle of a triangle is equal to the sum of the two opposite interior angles. This property of Lines and Angles is used in many geometric proofs and calculations.