Practical Geometry

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.