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.

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

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

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 three side lengths using compasses

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

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

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

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 pair of compasses is used to draw an arc. The value of $$x$$ is {{ }}.

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?

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

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

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

Label point where arc meets the ray as B.

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

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.

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

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?

The triangles are neither similar nor congruent.

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

Lucas and Sofia both accurately construct triangles of sides 8 cm, 9 cm and 11 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 8.5 cm and 9.6 cm. The distance between their centres is 7.3 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 6 cm and needle of compasses on A.

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

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

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

Lesson outcome