Class 6 Notes - Practical Geometry

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1. Introduction to Practical Geometry

Practical Geometry is the branch of mathematics that deals with drawing geometric shapes accurately using instruments like a ruler, compass, protractor, and set squares. It is also called "Geometrical Constructions."

2. Instruments Used in Practical Geometry

  • Ruler: For drawing straight lines and measuring lengths.
  • Compass: For drawing circles and arcs.
  • Protractor: For measuring and drawing angles.
  • Set Squares: For drawing perpendicular and parallel lines.
  • Pencil and Eraser: For neat and accurate constructions.

3. Basic Constructions

  • Drawing a line segment of a given length.
  • Copying a line segment.
  • Bisecting a line segment (finding its midpoint).
  • Constructing the perpendicular bisector of a line segment.
  • Drawing a perpendicular to a line from a point on the line.
  • Drawing a perpendicular to a line from a point outside the line.
  • Constructing an angle of a given measure using a protractor.
  • Copying an angle.
  • Bisecting an angle.
  • Drawing the perpendicular bisector of an angle.

4. Construction of Triangles

Triangles can be constructed when certain measurements are given:

  • Three sides (SSS)
  • Two sides and the included angle (SAS)
  • Two angles and the included side (ASA)
  • Right-angled triangle (RHS)

5. Steps for Construction (Example)

Example: Construct a triangle ABC with AB = 5 cm, BC = 6 cm, and AC = 4 cm.

  1. Draw a line segment AB = 5 cm using a ruler.
  2. With A as center and radius 4 cm, draw an arc.
  3. With B as center and radius 6 cm, draw another arc to cut the previous arc at C.
  4. Join AC and BC to complete the triangle.

6. Tips for Accurate Construction

  • Use sharp pencils for clear lines.
  • Keep the compass steady while drawing arcs.
  • Measure carefully with the ruler and protractor.
  • Label all points clearly.

7. Practice Exercises

  1. Draw a line segment of length 7 cm and bisect it.
  2. Construct an angle of 60° using a compass and ruler.
  3. Draw a triangle with sides 5 cm, 6 cm, and 7 cm.
  4. Construct the perpendicular bisector of a 6 cm line segment.
  5. Copy an angle of 45° from your textbook using a compass.

8. Summary

  • Practical Geometry involves drawing shapes using mathematical instruments.
  • Accuracy and neatness are important in constructions.
  • Practice helps in mastering the use of compass, ruler, and protractor.