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14.2.2 Constructing triangles

You have learnt the properties of the different types of triangles. Let us recall
some properties of the triangles to help us construct triangles. You will need a
ruler, a protractor and a compass.
Grouping triangles according to sides
Triangle A has 3 equal sides.
We name such a triangle an equilateral triangle.

Triangle D has 2 equal sides.
Triangle E also has 2 equal sides.
We name such triangles isosceles triangles.

Triangle B does not have any equal sides.
Triangles C and F also do not have any equal sides.
We name such triangles scalene triangles.

Grouping triangles according to angles
The angles of triangle A are all acute angles.
The angles of triangle D are also all acute angles.
We name such triangles acute-angled triangles.

Triangle C has an obtuse angle.
Triangle E also has one obtuse angle.
We name such triangles obtuse-angled triangles.

Triangle B has a right angle.
Triangle F also has a right angle.
We name such triangles right-angled triangles.

Constructing right-angled triangles

Example 5
Draw a sketch to help you.
Construct a triangle ABC such that AB = 5 cm, AC = 4 cm and ZCAS = 90°.

Solution
Draw a line AS = 5 cm. Using a compass, draw an
1 2. arc 4 cm from A.

5 cm

5 cm

UNIT 14 Geometrical Constructions