Support the Monkey! Tell All your Friends and Teachers

Help / FAQ




Win a $1000 or more Scholarship to college!


Please Take our User Survey


1.5 Angles made by a transversal

Definition of a transversal : A line which intersects two or more given coplanar lines in distinct points is called a transversal of the given lines. In figure 1.24 the line l is the transversal of lines a and b.

Figure 1.24

l intersects a and b at P and Q respectively. The three lines determine eight angles four with vertex P and the remaining four with vertex Q.

Corresponding angles : Angles that appear in the same relative position in each group are called corresponding angles, i.e. Ð 1 and Ð 5 are called corresponding angles. Similarly Ð 2 & Ð 6, Ð 4 & Ð 8 and Ð 3 & Ð 7 are pairs of corresponding angles.

Interior and Exterior angles : Those angles which lie between lines a and b are called interior angles, i.e. Ð 3, Ð 4, Ð 5 and Ð 6 . Exterior angles lie on opposite sides of lines a and b, i.e. Ð 1, Ð2, Ð 7 and Ð 8 .

Alternate and Consecutive Interior angles : Interior angles on opposite sides of the transversal are called alternate interior angles and Ð 4, Ð 6 are alternate interior angles and so also Ð 3, and Ð 5 .

Interior angles on same side of the transversal are called consecutive interior angles. Ð 4, and Ð 5 are consecutive interior angles and so also Ð 3 and Ð 6 .

Alternate and Consecutive Exterior angles : Alternate exterior angles are on opposite sides of the transversal and do not lie between lines a and b, i.e. Ð 1 and Ð 7 and also Ð 2 and Ð 8 .

Exterior angles on the same side of the transversal are called consecutive exterior angles, i.e. Ð 1 & Ð 8 as also Ð 2 and Ð 7 .

Example 1

In figure 1.25 n is the transversal of lines l and m. Write down the pairs of :

a) corresponding angles ,

b) alternate interior angles,

c) alternate exterior angles ,

d) consecutive interior angles & ,

e) consecutive exterior angles.

Figure 1.25

Answers

a) Ð a & Ðe , Ð b & Ð f , Ð c & Ð g , Ð d & Ð h .

b) Ð d & f , Ð c & Ð e

c) Ð a & Ð g , Ð b & Ð h

d) Ð f & Ð c , Ð d & Ð e

e) Ð a & Ð h , Ð b & Ð g .

 

Index

Introduction

1.1 Points, Lines and Planes
1.2 Line Segment
1.3 Rays and Angles
1.4 Some Special Angles
1.5 Angles made by a Transversal
1.6 Transversal Across Two Parallel Lines
1.7 Conditions for Parallelism

Chapter 2

All Contents Copyright © All rights reserved.
Further Distribution Is Strictly Prohibited.


Search:
Keywords:
In Association with Amazon.com