# Lines and Angles

## Contents

## Concept Lectures

Session # 1 : Introduction: Definition of Lines and Angles, Vertex and sides of an angle, Interior and Exterior of an Angle

Session # 2 : Different ways of measuring and angle, a) Sexagesimal System, b) Circular Measure, c) Centesimal System

Session # 3 : Degrees, Minutes and Seconds, Concept of Negative Angle, Axioms related to Angles

Session # 4 : Types of Angles: Acute, Right, Obtuse, Straight, Reflex and Complete Angles; Angles measuring more than 360 degrees.

Session # 5 : Complementary Angles, Supplementary Angles and Angle Bisectors

## Solved Examples

Session # 6 : Solved Example # 01: Two Problems On Supplementary Angles

Session # 7 : Solved Example # 02: Two Problems On Supplementary Angles

## Concept Lectures

Session # 8 : Angle Relations: Adjacent angles and Linear Pair

Session # 9 : Linear Pair Theorem: Sum of Angles forming a Linear Pair = 180º

Session # 10: Converse of Linear Pair Theorem: If two adjacent angles sum up to 180º then the non-common arms are opposite to each other.

Session # 11: Sum of angles around a point is 360º

## Solved Examples

Session # 12: Solved Example # 03: On Linear Pairs

Session # 13: Solved Example # 04: On Linear Pairs

Session # 14: Solved Example # 05: On Linear Pairs

## Concept Lectures

Session # 15: Vertically Opposite Angles are equal

## Solved Examples

Session # 16: Solved Example # 06: On Vertically Opposite Angles

## Concept Lectures

Session # 17: Transversal intersecting two coplanar lines. Definitions of Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles and Adjacent Angles

Session # 18: Corresponding Angle Axiom: Corresponding angles of parallel lines intersected by a transversal are equal.

Session # 19: Alternate Interior Angles Theorem and Its Converse

Session # 20: Consecutive Interior Angles are supplementary

Session # 21: Bisectors of Alternate Interior Angles are Parallel

Session # 22: Bisectors of Corresponding Angles are Parallel

Session # 23: A line perpendicular to one of two parallel lines is also perpendicular to the other line

## Solved Examples

Session # 24: Solved Example on parallel lines, transversals and associated angles

Session # 25: Solved Example on parallel lines, transversals and associated angles

Session # 26: Solved Example on parallel lines, transversals and associated angles

Session # 27: Solved Example on parallel lines, transversals and associated angles

Session # 28: Solved Example on parallel lines, transversals and associated angles

Session # 29: Solved Example on parallel lines, transversals and associated angles

Session # 30: Solved Example on parallel lines, transversals and associated angles

Session # 31: Solved Example on parallel lines, transversals and associated angles

Session # 32: Solved Example on parallel lines, transversals and associated angles