CBSE Class 9 Maths Notes Chapter 6 Lines and Angles

CBSE Class 9 Maths Notes Chapter 6: In Chapter 6 of CBSE Class 9 Maths, we learn about "Lines and Angles." This chapter helps us understand the basics of lines and angles. We explore different types of angles like complementary, supplementary, adjacent, and vertically opposite angles.

CBSE Class 9 Maths Notes Chapter 6 Lines and Angles Overview

CBSE Class 9 Maths Notes Chapter 6 PDF

CBSE Class 9 Maths Notes Chapter 6 PDF

CBSE Class 9 Maths Notes Chapter 6 Lines and Angles

Point

• A point is a precise location in space, often represented by a dot.
• It has no length, width, or thickness but defines a specific position.
• Points are denoted by capital letters like A, B, C, O, etc.

Line Segment

• A line segment, represented as AB¯¯¯¯¯¯¯¯, is a straight path connecting two points, A and B.
• It has a defined length and two endpoints, but no width or thickness.

Ray

• A ray is a portion of a line that starts at a particular point (called the endpoint) and extends infinitely in one direction.
• It is represented by a line segment with an arrowhead at one end.

Line

• A line is formed when a line segment is extended infinitely in both directions.
• It has no endpoints and continues indefinitely in both directions.

Collinear Points

• Collinear points are points that lie on the same straight line.
• For example, if points A, B, and C are on the same line, they are said to be collinear.
• In a plane, any two distinct points determine a unique line, and three or more points can be collinear if they all lie on the same line.

Non-collinear Points

• Non-collinear points are points that do not lie on the same straight line.
• In other words, if you cannot draw a single straight line passing through all the points, they are non-collinear.
• For example, points A, B, C, D, and E are non-collinear.

Intersecting Lines

• Intersecting lines are two lines that meet or cross each other at a common point.
• This common point is called the point of intersection.
• Each line has an infinite number of points, but only one of those points is shared by both lines.

Concurrent Lines

• Concurrent lines are lines that intersect or meet at the same point.
• This point of intersection is common to all the lines.
• In a plane, if two or more lines share a common point of intersection, they are concurrent.

Plane

• A plane is a flat surface that extends infinitely in all directions.
• It is defined by any three non-collinear points or a line and a point not on the line.
• Examples of planes include the surface of a smooth wall, a piece of paper, or a tabletop.
• Any two points within a plane can be connected by a straight line, and any line segment lying entirely in the plane can be extended indefinitely to form a line.

Angles

Vertex: The common endpoint of the two rays or line segments forming the angle.

Arms: The two rays or line segments that form the angle.

Types of Angles:

• Acute Angle: An angle whose measure is greater than 0° and less than 90°.
• Right Angle: An angle whose measure is exactly 90°.
• Obtuse Angle: An angle whose measure is greater than 90° and less than 180°.
• Straight Angle: An angle whose measure is exactly 180°.
• Reflex Angle: An angle whose measure is greater than 180° and less than 360°.
• Full Angle: An angle whose measure is exactly 360°.

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

1. Complementary Angles: Two angles whose measures add up to 90°.
2. Supplementary Angles: Two angles whose measures add up to 180°.
3. Vertical Angles: Two angles formed by intersecting lines, where each angle's arms are opposite rays. They are congruent to each other.

Bisector of an Angle

Parallel Lines