Lines and Angles

Introduction

• Chapter 5 in NCRT book.
• Instructor: Abhishek Kumar
• Focus on the concepts of lines and angles.

Key Concepts

Lines and Line Segments

• Lines: Created by extending a dot in both directions without lifting the pen.
• Line Segment: A portion of a line with two endpoints (e.g., segment PQ).
• Ray: A part of a line that has one endpoint and extends infinitely in one direction.

Identifying Angles

• An angle is formed when two lines or line segments meet.
• Example: Angle POS, where O is the vertex.
• Always write the vertex in the center when naming angles (e.g., angle AOB).

Types of Angles

Complementary Angles

• Definition: Two angles whose measures sum up to 90 degrees.
• Example: 40° and 50° are complementary.

Supplementary Angles

• Definition: Two angles whose measures sum up to 180 degrees.
• Example: 60° and 120° are supplementary.

Adjacent Angles

• Definition: Two angles that share a common vertex and a side but do not overlap.
• They have a common arm.

Linear Pair

• Definition: A pair of adjacent angles formed when two lines intersect, whose non-common sides form a straight line.
• Always supplementary (sum is 180 degrees).

Vertically Opposite Angles

• Definition: Angles opposite each other when two lines cross.
• They are always equal.

Properties of Parallel Lines Cut by a Transversal

1. Corresponding Angles: Equal when a transversal cuts parallel lines.
2. Alternate Interior Angles: Equal when a transversal cuts parallel lines.
3. Interior Angles on Same Side of Transversal: Supplementary (sum is 180 degrees).

Example Problems

• Deductions related to angles based on given properties.
• Verifying whether lines are parallel based on angle measurements.

Conclusion

• Understanding lines and angles is fundamental for geometry.
• The concepts of complementary and supplementary angles help in solving problems related to angles.
• Keep practicing the identification and properties of angles for better grasp in higher classes.