Learning Objectives
- Learn to use a ruler, compass, protractor, and set squares
- Construct a circle with a given radius
- Construct a line segment of a given length and its copy
- Construct perpendicular lines and perpendicular bisectors
- Construct angles of given measures and angle bisectors
Key Concepts
Geometric Tools
The basic tools for geometric construction are: a ruler for drawing and measuring straight lines; a compass for drawing circles and arcs; a protractor for measuring and drawing angles; and set squares (30°-60°-90° and 45°-45°-90°) for drawing specific angles and parallel lines. A divider is used for measuring lengths accurately.
Constructing a Circle
Open the compass to the desired radius using a ruler. Place the pointed end firmly on the paper as the centre. Rotate the pencil end fully around to draw the circle. Keep the compass opening steady while drawing.
Constructing a Line Segment
To draw a line segment of a given length, mark a point, place the ruler with 0 at that point, and mark another point at the desired length. Join the two points. To copy a line segment, use a compass to measure the original segment's length, then draw an arc from a new point.
Perpendicular Bisector
A perpendicular bisector of a line segment passes through the midpoint and makes a 90° angle with it. To construct it: (1) Take the compass with radius more than half the segment. (2) Draw arcs from both endpoints on both sides of the line. (3) The arcs intersect at two points. (4) Join these two points to get the perpendicular bisector.
Constructing Angles
Using a protractor: Place the centre of the protractor at the vertex. Align the base line with one arm. Mark the desired angle and draw the other arm.
Special angles using compass: 60° can be constructed using a compass by drawing an equilateral triangle's angle. 90° is constructed using the perpendicular bisector method. 120° = 2 × 60°. 30° is the bisector of 60°. 45° is the bisector of 90°.
Angle Bisector
An angle bisector divides an angle into two equal parts. To construct it: (1) With vertex as centre, draw an arc cutting both arms. (2) From the points where the arc meets the arms, draw two arcs of equal radius intersecting each other. (3) Join the vertex to the intersection point — this is the angle bisector.
Summary
Practical geometry teaches us to construct shapes and lines accurately using tools. We learn to draw circles, line segments, perpendiculars, and angles. The compass and ruler are the most important tools. Constructions of perpendicular bisectors and angle bisectors are fundamental skills. Special angles like 30°, 45°, 60°, 90°, and 120° can be constructed using only a compass and ruler.
Important Terms
- Compass: A tool for drawing circles and arcs of a given radius
- Protractor: A tool for measuring and drawing angles
- Perpendicular Bisector: A line that cuts a segment into two equal parts at 90°
- Angle Bisector: A ray that divides an angle into two equal angles
- Arc: A part of a circle drawn using a compass
- Construction: Drawing geometric figures accurately using mathematical tools
Quick Revision
- Use a compass and ruler for accurate constructions, not freehand drawing
- A perpendicular bisector passes through the midpoint at 90°
- An angle bisector divides an angle into two equal halves
- 60° angle: draw an arc from the vertex, then from the intersection draw another arc with same radius
- 30° = half of 60°; 45° = half of 90°; 120° = 60° + 60°
- Keep the compass opening fixed while drawing arcs for constructions
- Always use sharp pencils for accurate constructions