Mathematics Class 7 - Lines And-Angles Notes

Lines and Angles

Welcome to the chapter on Lines and Angles for Class 7. In this chapter, you will learn about different types of lines, angles, their properties, and how to solve problems related to them. By the end of this chapter, you will be able to identify, measure, and use lines and angles in geometry confidently!

Introduction

Lines and angles are basic concepts in geometry. They help us understand shapes, figures, and how objects relate to each other in space.

Types of Lines

• Line: A straight path that goes on forever 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 on forever in one direction.
• Parallel Lines: Lines that never meet, no matter how far they are extended.
• Intersecting Lines: Lines that cross each other at one point.
• Perpendicular Lines: Lines that meet at a right angle (90°).

Types of Angles

• Angle: Formed when two rays meet at a common endpoint (vertex).
• 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.
• Vertically Opposite Angles: Angles opposite each other when two lines intersect; they are always equal.

Properties and Theorems

• Vertically opposite angles are equal.
• Sum of angles on a straight line is 180°.
• Sum of angles around a point is 360°.
• If two lines are perpendicular, they form four right angles.

Measuring Angles

Use a protractor to measure angles. Place the center at the vertex and read the degree where the other arm points.

Fun Activity: Angle Hunt!

Look around your classroom or home. Find examples of different types of angles and lines. Draw and label them in your notebook!

Summary

• Lines can be straight, parallel, intersecting, or perpendicular.
• Angles can be acute, right, obtuse, straight, or reflex.
• Pairs of angles include complementary, supplementary, adjacent, and vertically opposite angles.
• Use a protractor to measure angles.

Practice Questions

1. Define a line segment and a ray.
2. What is a right angle?
3. Name two pairs of supplementary angles.
4. If two lines intersect, what can you say about the vertically opposite angles?
5. Draw and label an acute, obtuse, and reflex angle.

Challenge Yourself

• Find three objects at home that show parallel lines.
• Measure three angles in your classroom using a protractor.

Did You Know?

• The hands of a clock make different angles at different times!
• The corner of a square or rectangle is a right angle.

Glossary

• Line: A straight path that goes on forever.
• Angle: The space between two rays meeting at a point.
• Vertex: The common endpoint of two rays forming an angle.
• Protractor: A tool used to measure angles.

Answers to Practice Questions

1. A line segment has two endpoints; a ray has one endpoint and goes on forever in one direction.
2. An angle of 90°.
3. Angles of 120° and 60°, 150° and 30° (any two pairs that add up to 180°).
4. Vertically opposite angles are equal.
5. (Drawings will vary; acute: less than 90°, obtuse: more than 90° but less than 180°, reflex: more than 180°).

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Practice drawing and measuring lines and angles to become a geometry expert!