Lines and Angles: Geometry Introduction

Today I am start Geometry series. In this series I will share all the basic rules and techniques to solve questions from this chapter.


Geometry basics

Complementary Angles:

Two angles whose sum is 90 degree are called Complementary Angles.

For example 40 degree and 50 degree

Their sum =40 degree +50 degree= 90 degree

Supplementary Angles:

Two angles whose sum is 180 degree are called Supplementary Angles.

For example 100 degree and 80 degree

Their sum =100 degree + 80 degree= 180 degree

Linear pairs:

Two angles on a given line are called linear if their sum is 180 degree. Look at the picture below.

linear pair
In the above figure angle ABD and angle CBD are linear pair because their sum is 180 degree.

Vertically opposite Angles: 

Vertically opposite angles are formed when two lines, say AB and CD intersect each other at a point O. There are two pairs of vertically opposite angles and they are always equal.


Vertically opposite Angles:

One pair is angle AOD and angle COB

Angle AOD = Angle COB (Vertically opposite angles)

The other pair is angle AOC and angle BOD

Angle AOC = Angle BOD ( Vertically opposite angles)

Note : If two lines intersect each vertically opposite angles are equal.

Transversal

A line which intersects two or more lines at different points is called a transversal.

Let us understand this:


Transversal
In the above picture line l intersects lines m and n at points P and Q respectively. Thus line l is a transversal for lines m and n. By observing the picture, we can see that there are four angles formed at each point P and Q.

Angle 1 , Angle 2 , Angle 7, Angle 8 are called exterior angles, while Angle 3, Angle 4, Angle 5 and Angle 6 are called interior angles.

Corresponding Angles:

  • Angle 1 and Angle 5 
  • Angle 2 and Angle 6 
  • Angle 4 and Angle 8 
  • Angle 3 and Angle 7

Alternate Interior Angles

  • Angle 4 and Angle 6 
  • Angle 3 and Angle 5

Alternate Exterior Angles

  • Angle 1 and Angle 7 
  • Angle 2 and Angle 8

Interior Angles on the same side of the transversal

  • Angle 4 and Angle 5 
  • Angle 3 and Angle 6




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