Practical Geometry

1. Introduction to Practical Geometry

Practical Geometry is the branch of geometry that deals with the construction of geometrical figures using instruments such as a ruler, compass, protractor, and set squares. In Class 7, students learn to construct various shapes and angles accurately.

2. Geometrical Instruments

• Ruler: Used to draw straight lines and measure lengths.
• Compass: Used to draw arcs and circles.
• Protractor: Used to measure and draw angles.
• Set Squares: Used to draw perpendicular and parallel lines.
• Pencil and Eraser: For drawing and corrections.

3. Basic Constructions

• Constructing a line segment of a given length.
• Constructing a copy of a given line segment.
• Constructing the perpendicular bisector of a line segment.
• Constructing an angle of a given measure using a protractor.
• Constructing a copy of a given angle using a compass.
• Bisecting a given angle.
• Constructing angles of special measures (30°, 45°, 60°, 90°, 120°) using compass and ruler.
• Drawing perpendicular lines from a point on the line and from a point outside the line.
• Drawing parallel lines to a given line through a point.

4. Steps of Construction (Examples)

4.1 Constructing a Perpendicular Bisector

1. Draw a line segment AB of given length.
2. With A as center and radius more than half of AB, draw arcs above and below the line.
3. With B as center and the same radius, draw arcs to intersect the previous arcs.
4. Mark the intersection points as P and Q. Join PQ. PQ is the perpendicular bisector of AB.

4.2 Constructing an Angle of 60°

1. Draw a ray OA.
2. With O as center, draw an arc to cut OA at B.
3. With B as center and the same radius, draw an arc to cut the first arc at C.
4. Join OC. ∠AOC = 60°.

5. Practice Activities

• Construct a triangle with given sides using ruler and compass.
• Draw a perpendicular from a point to a line.
• Construct an angle of 90° without using a protractor.
• Draw parallel lines using set squares.

6. Common Mistakes

• Not keeping the compass radius fixed while drawing arcs.
• Not marking intersection points clearly.
• Using blunt pencils, leading to inaccurate constructions.
• Not labeling points properly.

7. Word Problems

1. Construct a line segment of length 7 cm and bisect it. What is the length of each part?
2. Draw a triangle with sides 5 cm, 6 cm, and 7 cm. Measure all angles using a protractor.
3. Construct an angle of 120° and bisect it. What is the measure of each angle?

8. Summary

• Practical geometry involves constructing shapes and angles using instruments.
• Accuracy and neatness are important for correct constructions.
• Practice helps in mastering the use of geometrical tools.