Constructing a triangle given three side lengths using compasses | Maths

Starter quiz

Supplementary angles are a pair of angles that sum to ______°.

'180' ✓
The diagram shows the perpendicular bisector of AB that passes through the point P. The perpendicular intersects AB at point O. Which of these constructions will produce a 45° angle?

The angle bisector of BOP. ✓

The angle bisector of APB.

The angle bisector of AOP. ✓

The perpendicular bisector of OB.

The perpendicular bisector of OP.
EC is a perpendicular to AD. The angle AOC is bisected. Match each angle to its size.

Angle AOB

⇔

45° ✓

Angle BOD

⇔

135° ✓

Angle COD

⇔

90° ✓

Reflex angle BOD

⇔

225° ✓

Reflex angle BOC

⇔

315° ✓
The line segments AB and BC form an angle of 120°. Which of these constructions creates a 60° angle?

The perpendicular bisector of AB

A perpendicular to BC through C

An angle bisector of the angle ABC ✓

An extension of BC in the direction of B
Line segments AB and BC are the legs of a 136° angle. The diagram shows the two constructions that are applied to ABC. The angle $x$ ° is ______°.

'22' ✓
Line segments AB and BC are the legs of a 136° angle. The diagram shows the two constructions that are applied to ABC. The angle $z$ ° is ______°.

'112' ✓

Exit quiz

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

'9' ✓
What equipment do you need in order to accurately construct a triangle given the length of 3 sides?

A pair of compasses ✓

A protractor

A ruler ✓

A set square

A sharp pencil ✓
Jun is using GeoGebra to accurately draw a triangle with side lengths 6 units, 8 units and 10 units. Which of these tools should Jun use to draw the first side of the triangle?

a

b ✓

c

d
Jun and Izzy both accurately construct triangles of sides 6 cm, 7 cm and 9 cm. Which statement is correct?

The triangles could be congruent, but the angles need to be checked to be sure.

The triangles are definitely congruent. ✓

The triangles are definitely similar.

The triangles are neither similar nor congruent.
Here are two circles with centres A and B. The circles meet at C and D. The radius of the circles are 7.2 cm and 9.1 cm. The distance between their centres is 6.4 cm. Match each length to its value.

AB

⇔

6.4 cm ✓

CA

⇔

7.2 cm ✓

BD

⇔

9.1 cm ✓
Starting with the first step, put these instructions in the correct order to construct triangle ABC with sides 4 cm, 5 cm and 6 cm.

1

⇔

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

2

⇔

Set compasses to 4 cm and needle of compasses on A.

3

⇔

Draw a circle of radius 4 cm, centre A.

4

⇔

Repeat last 2 steps using B and 6 cm.

5

⇔

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

6

⇔

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

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
A pair of compasses should be used to indicate potential positions for the other sides, by drawing arcs
Where the two remaining sides intersect is where the two sides should be drawn to
All triangles with the same measurements are congruent

Common misconception

Pupils may try to draw the triangle using only a pencil and ruler, rather than construct it using a pair of compasses.

Remind pupils that if the task is to 'construct' then they must use their geometry equipment.

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.
Radius - The radius is any line segment that joins the centre of a circle to any point on its circumference.
Congruent - If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.
Arc - An arc is part of a curve. An arc of a circle is part of the circle’s circumference.