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Theorem : If two angles are complementary to equal angles they are equal to each other . If Ð a and Ð b are complementary to Ð c and Ð d respectively where m Ð c = m Ð d.

Proof : m Ð a + m Ð c = m Ð b + m Ð d = 900

m Ð a + m Ð c = m Ð b + m Ð d

Since m Ð c = m Ð d

m Ð a + m Ð c = m Ð b + m Ð c

or m Ð a = m Ð b.

Supplementary angles : If the measures of two angles sum up to 1800 they are called supplementary angles. Supplementary angles are of two types :

a) Non adjacent supplementary angles and

b) Adjacent supplementary angles.

Non adjacent supplementary angles are distinct and have no arm in common (figure 1.21).

Figure 1.21

Ð A and Ð B are supplementary and non adjacent.

Adjacent supplementary angles are called angles in a linear pair and have one arm in common ( figure 1.22 ).

Figure 1.22

Vertical angles : When two lines AB and CD intersect at O, four angles are formed with vertex O. Consider Ð AOC and Ð BOD. It is observed that and are opposite rays and so is and . In such a case Ð AOC and Ð BOD are called vertical angles ( figure 1.23 ).

Figure 1.23

 

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

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