Triangles – JSS2 Basic Technology Lesson Note (First Term)

A triangle is a plane figure bounded by three straight lines and having three angles. The sum of the angles in a triangle is 180°.

Behavioural objectives

1. Define a triangle and state the sum of its angles.
2. Name the four types of triangle and describe each one.
3. Construct a triangle given three sides.
4. Construct a triangle given two sides and the included angle.
5. Construct an equilateral triangle using compasses.

What are the parts of a triangle?

A triangle has three sides, three angles and three corner points.

• Side: each of the three straight lines that bound the triangle.
• Vertex: a corner where two sides meet. A triangle has three vertices, usually named A, B and C.
• Angle: the opening between two sides at a vertex.
• Base: the side on which the triangle is taken to stand, usually drawn horizontally.
• Included angle: the angle between two given sides. In triangle ABC, the angle at A is included between AB and AC.

What is the sum of the angles in a triangle?

The three angles of any triangle add up to 180°.

• Rule: angle A + angle B + angle C = 180°.
• Finding a missing angle: subtract the two known angles from 180°.
• Example 1: if two angles are 50° and 60°, the third is 180° − 110° = 70°.
• Example 2: in a right-angled triangle with one angle of 35°, the third angle is 180° − 90° − 35° = 55°.

What are the types of triangles?

There are four types of triangle taught at this level: scalene, isosceles, equilateral and right-angled.

Scalene triangle

• Meaning: a triangle that has none of its sides or angles equal.
• Example: a triangle with sides 8 cm, 7 cm and 6 cm.

Isosceles triangle

• Meaning: a triangle that has two sides and two angles equal.
• Equal angles: they are the angles opposite the two equal sides.
• Example: a triangle with sides 5 cm, 5 cm and 3 cm.

Equilateral triangle

• Meaning: a triangle that has all three sides and all three angles equal.
• Size of each angle: 180° ÷ 3 = 60°.
• Example: a triangle with three sides of 6 cm each.

Right-angled triangle

• Meaning: a triangle in which one of the angles is 90°.
• Hypotenuse: the longest side, which faces the 90° angle.
• Other two angles: they add up to 90°.
• Example: the corner of a set square.

How do the four types compare?

Where are triangles used?

Triangles are used in building and technical drawing because the shape is firm and does not easily change.

• Roof trusses: timber pieces arranged in triangles hold up a roof.
• Set squares: drawing tools shaped as right-angled triangles.
• Ladders: a ladder leaning on a wall forms a right-angled triangle with the ground.
• Gable ends: the triangular top of a wall under a sloping roof.

What tools are needed to construct triangles?

Constructing a triangle needs simple drawing instruments and a sharp pencil.

• Ruler: draws straight lines and measures lengths.
• Pair of compasses: strikes arcs of a given radius.
• Protractor: measures and marks angles.
• Sharp pencil: gives thin, accurate lines.

How do you construct a triangle given the three sides?

Draw one side as the base, then use compasses to find the point where the other two sides meet.

1. Draw a horizontal line and mark off the base of the triangle, AB.
2. With centre A and a radius equal to the length of one of the other sides, strike an arc.
3. With centre B and a radius equal to the remaining side, strike another arc to cut the first one at C.
4. Join CA and CB to obtain the triangle ABC.

• Check: the two shorter sides together must be longer than the longest side, or the arcs will not meet.
• Example: for AB = 8 cm, BC = 7 cm and AC = 6 cm, 7 + 6 = 13, which is more than 8.

How do you construct a triangle given two sides and the included angle?

Draw one side, make the given angle at one end of it, then cut off the second side along the angle line.

1. Draw a horizontal line and mark off one of the given sides, AB.
2. At A, construct the given included angle BAC with the aid of a protractor.
3. With centre A and a radius equal to the other given side of the triangle, cut AC at D.
4. Join DB to complete the required triangle ABD.

• Tip: make the angle at the vertex where the two given sides meet.

How do you construct an equilateral triangle using compasses?

Use the same compass opening, equal to the given side, for every arc.

1. Draw a horizontal line and mark off the base AB equal to the given side.
2. With centres A and B and a radius equal to the given side, strike arcs to intersect at C.
3. Join CA and CB to obtain the required equilateral triangle.

• Check: each angle should measure 60° with a protractor.

Evaluation

1. What is a triangle?
2. List the types of triangles and describe them.
3. Construct triangle ABC such that AB is 8 cm, BC is 7 cm and AC is 6 cm.
4. Construct triangle ABC such that line AB is 5 cm, angle ABC is 60° and line BC is 7 cm.
5. Construct an equilateral triangle whose sides are 6 cm long.

Assignment

Draw one example of each of the four types of triangle. Label each drawing with its name and write one sentence describing it.