Lines and Angles

Board: GSEB Class: 9

Chapter Overview

An angle is formed by two rays with a common endpoint. Types: acute (< 90°), right (= 90°), obtuse (> 90° and < 180°), straight (= 180°), reflex (> 180°), and complete (= 360°). Complementary angles sum to 90°, supplementary angles sum to 180°. Adjacent angles share a vertex and a side. Linear pair: adjacent angles whose non-common sides are opposite rays (sum = 180°). Vertically opposite angles are equal. Parallel lines and transversals: corresponding angles, alternate interior angles, and interior angles on the same side of the transversal.

Topics Covered

Angle Types
Complementary and Supplementary
Adjacent and Linear Pair
Vertically Opposite Angles
Parallel Lines
Transversal
Corresponding Angles
Alternate Angles
Interior Angles

Key Formulas

Complementary: A + B = 90°

Supplementary: A + B = 180°

Vertically opposite angles are equal

If AB || CD, corresponding angles are equal

If AB || CD, alternate interior angles are equal

Real-World Applications

Applications: Construction, navigation, carpentry, surveying, architectural design, engineering.

Study Tips

Tip: Learn angle pair relationships with diagrams

Tip: Practice parallel line proofs step by step

Tip: Draw figures for every problem