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.

The radius is any line segment that joins the centre of a circle to any point on its circumference.

If one shape can fit exactly on top of another using rotation, reflection or translation, then the shapes are congruent.

An arc is part of a curve. An arc of a circle is part of the circle’s circumference.

Constructing a triangle given three side lengths using compasses

Maths

Checking and securing understanding of constructing the perpendicular bisector of a line segment

Checking and securing understanding of constructing a perpendicular to a given line through a point

Checking and securing understanding of bisecting an angle

Constructing angles of  90° and 45°

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

Constructing a triangle given two angles and the side length between them

Constructing a right-angled triangle given the length of the hypotenuse and one other side length

Constructing a triangle given two side lengths and an angle not between them

Constructing loci

Applying constructions to loci problems

Solving loci problems in context

Advanced problem solving with loci and constructions

The constructions covered in the prior unit are built on in this unit. In this unit, pupils construct triangles and construct diagrams following specific restrictions.

In this unit, pupils construct triangles and construct diagrams following specific restrictions using their knowledge of loci and their work on constructions.

Loci and construction

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.

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

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?

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

The triangles are neither similar nor congruent.

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

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.

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

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

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

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.

Supplementary angles are a pair of angles that sum to {{}}°.

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?

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

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

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 {{ }}°. 

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 {{ }}°. 

Constructing a triangle given three side lengths using compasses

Lesson outcome