lines & angles

LINES & ANGLES

Prepared By: Keshav Gupta

Class : 9th ARoll No. : 16

Introduction Lines Type of Lines Example of Lines Angles Type of Angles Example of Angles

CONTENTS

INTRODUCTION Lines and Angles are used in our daily

life

Lines and Angles are linked with each other

Angles have different properties depends on how the two lines are intersecting with each other

LINES We require minimum Two Points to draw a

Line Line can be extended through both the

ends Line with Two End Points is called Line-

Segment Line with One End Point is called Ray Line has No thickness and has only Length Three or more points lie on the same line

are called Collinear Points

Type of lines There are two types of Lines :

Intersecting LinesNon-Intersecting Lines [Parallel Lines]

Intersecting linesThe Lines which intersect each other at a point are

called Intersecting Lines.Intersecting lines forms angles at their intersecting

point.Example :a) Fig. 1 shows two line intersecting and forming an angleb) Fig. 2 shows two lines intersecting and forming an Right Angle, these type of lines are called Perpendicular Lines.

Parallel linesIf the distance between the two lines at

each point is same, then those lines are called Parallel Lines

Example:The distance between Points A & C and B

& D are same

Angles

An Angle is formed when two rays originate from same end point.

The Rays making an angle are called the arms of Angle and the end points are called Vertex of the angle.

Types of Angles Acute Angle Obtuse Angle Right Angle Straight Angle Reflex Angle Complementary Angles Supplementary Angles/Linear Pair Adjacent Angles Corresponding Angles Vertical Opposite angles Alternate Interior angles Alternate exterior angles

Acute Angles

The measure of an angle with a measure between 0° and 90° or with less than 90° radians.

60° 48° 87°

Right Angle

The measure of an angle with a measure of exact 90° is called Right Angle

90°

This angle is formed by the perpendicular intersection of two straight lines.

Obtuse Angles The measure of an angle with a measure

between 90° and 180° or with more than 90° radians.

120° 168° 95°

Straight Angle The measure of an angle with a measure

of exact 180° is called Straight Angle

180°

It looks like a straight line. It measures 180° (half a revolution, or two right angles)

Examples of Angles shown in previous slides

Reflex Angles

The measure of an angle with a measure between 180° and 360° or with less than 360° radians.

Complementary Angles When two angles whose sum is 90° are called

complementary Angles.

Angle ‘a’ and Angle ‘b’ are complementary angles

Supplementary /Linear Pair of Angles When two angles whose sum is 180° are

called Supplementary Angles or Linear Pair of Angles.

Angle ‘a’ and Angle ‘b’ are Supplementary angles and also they form Linear Pair.

Adjacent Angles

Adjacent Angles are formed when two angles haveA common vertexA common armThe non-common arms are on different

sides of common arm

Transversal

A line that intersects two lines at different points.

Corresponding Angles The Angles that occupy the same relative

position at each intersection where a straight line crosses two others.

If the two lines are parallel, the corresponding angles are equal.

Vertical Opposite Angles The Angles formed when two lines

intersect each other at a point. The vertically opposite angles are equal.

Alternate Interior Angles Two angles that lie between two lines on

opposite sides of the transversal are Alternate interior angles.

If the two lines are parallel, then Alternate interior angles are equal.

Alternate Exterior Angles

Two angles that lie outside two lines on opposite sides of the transversal are Alternate exterior angles.

If the two lines are parallel, then Alternate exterior angles are equal.