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Mathematics Class 8 - Constructions Notes

Comprehensive study notes for Class 8 - Constructions olympiad preparation

Constructions

Welcome to the chapter on Constructions for Class 8. In this chapter, you will learn how to draw geometric shapes and figures using a ruler and compass. By the end of this chapter, you will be able to construct angles, triangles, perpendicular bisectors, and more with accuracy and confidence!

Introduction

Constructions in geometry mean drawing shapes, angles, and lines using only a ruler and compass. These tools help us make precise drawings without measuring with a protractor.

Tools Needed

  • Ruler (scale)
  • Compass
  • Pencil
  • Eraser

Basic Constructions

  • Constructing a line segment of given length
  • Constructing an angle of given measure (using compass)
  • Bisecting a line segment
  • Bisecting an angle
  • Drawing perpendicular bisector of a line segment
  • Drawing perpendicular from a point to a line

Constructing Triangles

You can construct triangles when given:

  • Three sides (SSS)
  • Two sides and the included angle (SAS)
  • Two angles and the included side (ASA)

Example: Construct a triangle with sides 5 cm, 6 cm, and 7 cm.

Steps for Construction

  • Read the question carefully.
  • Draw the base using a ruler.
  • Use compass to mark lengths and angles.
  • Join the points to complete the figure.
  • Label all points clearly.

Fun Activity: Compass Art

Use your compass to draw circles and patterns. Try making a flower or a star using only circles!

Summary

  • Constructions use ruler and compass for accurate drawings.
  • You can construct angles, bisectors, and triangles.
  • Follow steps carefully for neat and correct figures.

Practice Questions

  1. Construct a line segment of length 8 cm.
  2. Bisect a line segment of 6 cm.
  3. Construct an angle of 60° using compass.
  4. Draw the perpendicular bisector of a 5 cm line segment.
  5. Construct a triangle with sides 4 cm, 5 cm, and 6 cm.

Challenge Yourself

  • Construct a triangle when two sides and the included angle are given.
  • Draw a perpendicular from a point outside a line.

Did You Know?

  • Ancient mathematicians used only ruler and compass for all constructions!
  • You can draw perfect circles with a compass.

Glossary

  • Compass: A tool to draw circles and arcs.
  • Bisector: A line that divides something into two equal parts.
  • Perpendicular: A line at 90° to another line.
  • Triangle: A shape with three sides and three angles.

Answers to Practice Questions

  1. Draw a straight line of 8 cm using a ruler.
  2. Draw a 6 cm line, then use compass to bisect it at 3 cm.
  3. Draw a base line, use compass to construct 60° angle.
  4. Draw a 5 cm line, use compass to find midpoint and draw perpendicular bisector.
  5. Draw base 4 cm, use compass to mark 5 cm and 6 cm from ends, join points to form triangle.

Practice constructions to improve your geometry skills and make perfect shapes!

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