Constructing a triangle given two side lengths and the angle between them using a compass | Maths

Starter quiz

Andeep sets his compasses to the width shown in the diagram. Without changing the setting, Andeep draws a circle. The diameter of the circle is ______ cm.

'10' ✓
What equipment do you need in order to accurately construct a perpendicular bisector?

A calculator

A pair of compasses ✓

A protractor

A ruler ✓

A sharp pencil ✓
Sofia is using GeoGebra to accurately draw a triangle with side lengths 6 units, 8 units and 10 units. Which of these tools should Sofia use to find the points where her two circles intersect?

a ✓

b

c

d
Lucas and Sofia both accurately construct triangles of sides 8 cm, 9 cm and 11 cm. Which statement is correct?

The triangles are definitely similar.

The triangles are definitely congruent. ✓

The triangles are neither similar nor congruent.

The triangles could be congruent, but the angles need to be checked to be sure.
Here are two circles with centres A and B. The circles meet at C and D. The radius of the circles are 8.5 cm and 9.6 cm. The distance between their centres is 7.3 cm. Match each length to its value.

AB

⇔

7.3 cm ✓

CB

⇔

9.6 cm ✓

AD

⇔

8.5 cm ✓
Match each step to the correct instruction needed to construct a triangle ABC with sides 5 cm, 6 cm and 7 cm.

Step 1

⇔

Use a ruler to draw line of length 5 cm. Label line A and B ✓

Step 2

⇔

Set compasses to 6 cm and needle of compasses on A. ✓

Step 3

⇔

Draw a circle of radius 6 cm, centre A. ✓

Step 4

⇔

Repeat last 2 steps using B and 7 cm. ✓

Step 5

⇔

Label one of the points where the 2 circles intersect as C. ✓

Step 6

⇔

Use a ruler to join both A and B to C. ✓

Exit quiz

The diagram shows part of a protractor measuring an angle. What is the size of the angle?

68° ✓

72°

112°

128°
The diagram shows a protractor measuring an angle. What is the size of the angle?

64°

76°

116° ✓

124°
Jacob is using GeoGebra to accurately draw a triangle with side lengths 8 units, 9 units and an angle of size 67° between them. Which tool should Jacob use to construct the angle?

a ✓

b

c

d
A pair of compasses is used to draw an arc. The value of $x$ is ______.

'9' ✓
Jun draws a ray line and a circle with radius 5 units then marks their intersection with point C. Which line segment has a length of 5 units?

'AC' ✓
Starting with the first step, put these instructions in the correct order to construct triangle ABC.

1

⇔

Use a ruler to draw side AC of 9 cm.

2

⇔

Use a protractor to measure 48° at A and mark a faint point.

3

⇔

Draw a ray line through A to show direction of AB.

4

⇔

Set compasses to width of 8 cm and mark an arc on the ray.

5

⇔

Label point where arc meets the ray as B.

6

⇔

Use a ruler to connect C and B.

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

The first side can be drawn accurately with a ruler
The compass should be used to indicate potential positions for the remaining side
A protractor should be used to accurately measure the desired angle
The line to mark the required angle should be drawn to meet one of the potential positions for the remaining side
All triangles with the same measurements are congruent

Common misconception

Some pupils may not recognise that they have constructed congruent triangles to one and another.

Use a piece of tracing paper to show that the triangles are congruent to each other.

Keywords

Pair of compasses - A pair of compasses is a tool which can be used to draw circles and arcs. A pair of compasses is sometimes referred to just as a compass.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.