4.2 GEOMETRICAL CONSTRUCTIONS
Geometrical constructions involve drawing accurate shapes using only a ruler and a pair of compass. In this lesson, learners will explore how to bisect angles, construct special angles such as 90° and 60°, construct triangles, and construct circles step-by-step with guided video tutorials.
In this sub-strand, we will be dealing with construction that use a ruler and a pair of compass only.
4.2.1 BISECTING ANGLES.
Bisecting angles involves drawing a line that divides an angle into two equal angles.
The process of bisecting angles can be learned from the video below
4.2.2 CONSTRUCTION OF ANGLES USING A RULER AND A PAIR OF COMPASS ONLY.
In basic angles are 90°, and 60°. From these two angles, other many angles can be constructed. Here we will have youtube links to construction of different angles.
| Angle | Video |
|---|---|
| 90° | |
| 60° | |
| 45° | |
| 22.5° | |
| 30° | |
| 15° | |
| 75° | |
| 150° | |
| 105° | |
| 135° |
4.2.3 CONSTRUCTION OF TRIANGLES USING A RULER AND A PAIR OF COMPASS ONLY.
Example 4.11
Construct a triangle ABC in which BC = 6 cm, CA = 5 cm and AB = 4 cm. Measure angle ABC and angle ACB.
Example 4.12
Using a ruler and a pair of compass only, construct a right triangle ABC in which LC = 90° and LABC = 45°, CB = 5 cm. Measure AB.
Example 4.13.
Using a ruler and a pair of compass only, construct triangle ABC in which AB = 5 cm, LBAC = 30° and LABC = 75°. Measure AC and CB.
CONSTRUCTION OF CIRCLES.
A Circle is constructed using an instrument known as a compass. Construction of a circle given its center and radius is as shown.
A circle whose diameter line is given is constructed as shown below.
Exercise 4.2
1. Construct triangle ABC with AB = 10 cm, BC = 8 cm and AC = 5.5 cm.
Measure ∠ABC and ∠ACB.
∠ABC = °
∠ACB = °
2. Construct triangle JKL with ∠JKL = 45°, KL = 5 cm and JL = 8 cm.
Measure length JK.
3. Construct triangle CAR with ∠ACR = 30°, ∠CRA = 75° and CA = 7 cm.
Measure AR.
4. Construct triangle WXY with ∠XWY = 90°, WX = 6 cm and ∠WXY = 60°.
Measure the length XY.
5. Construct a right triangle XYZ in which ∠XYZ = 90°, XY = 5 cm and YZ = 7 cm.
Measure ∠ZXY.
Score: 0 / 5