Mathematics Notes for Class 9 Lines And-Angles

Lines and Angles

In this chapter, you will learn about lines, angles, their types, properties, and how they relate to each other. By the end of this chapter, you will be able to identify different lines and angles, understand their properties, and solve problems using these concepts.

Key Concepts

Line: A straight path that extends endlessly in both directions.
Line Segment: A part of a line with two endpoints.
Ray: A part of a line that starts at one point and goes endlessly in one direction.
Angle: Formed when two rays meet at a common endpoint called the vertex.

Types of Angles

Acute Angle: Less than 90°
Right Angle: Exactly 90°
Obtuse Angle: More than 90° but less than 180°
Straight Angle: Exactly 180°
Reflex Angle: More than 180° but less than 360°

Pairs of Angles

Complementary Angles: Two angles whose sum is 90°
Supplementary Angles: Two angles whose sum is 180°
Adjacent Angles: Angles that have a common vertex and a common arm.
Linear Pair: Adjacent angles whose non-common arms form a straight line (sum is 180°).
Vertically Opposite Angles: Angles opposite each other when two lines intersect; they are equal.

Properties and Theorems

The sum of angles on a straight line is 180°.
Vertically opposite angles are always equal.
If two lines intersect, the opposite angles are equal.
If two angles form a linear pair, they are supplementary.

Practice Questions

Name the types of angles formed by the following: 45°, 90°, 120°, 180°, 270°.
If two angles are complementary and one is 35°, what is the other angle?
If two angles are supplementary and one is 110°, what is the other angle?
Draw two intersecting lines and mark the vertically opposite angles.
Explain why the sum of angles in a linear pair is always 180°.

Challenge Yourself

Find two pairs of supplementary angles in your classroom objects.
Draw a figure showing three types of angles: acute, obtuse, and right.

Did You Know?

Angles are measured using a protractor.
The word "angle" comes from the Latin word "angulus," meaning "corner."

Glossary

Vertex: The common endpoint of two rays forming an angle.
Arm: Each ray forming an angle.
Protractor: A tool used to measure angles.

Answers to Practice Questions

45°: Acute, 90°: Right, 120°: Obtuse, 180°: Straight, 270°: Reflex
55° (because 90° - 35° = 55°)
70° (because 180° - 110° = 70°)
(Draw two lines crossing; mark the pairs of equal angles opposite each other.)
Because the two angles together form a straight line, which measures 180°.

Understanding lines and angles is the foundation of geometry. Practice drawing and measuring angles to master this topic!

Mathematics Class 9 - Lines And-Angles Notes