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

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 side lengths and the angle between them using a compass

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

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

A pair of {{}} is a tool which can be used to draw circles and arcs. 

Which construction should you use to create a right-angle?

Jacob is constructing a right-angled triangle and has drawn a line segment for one of its shorter sides. Which tool can be used to construct a perpendicular line through one of its points?

The diagram shows a right-angled triangle constructed from two circles. The length of the hypotenuse is {{ }} cm.

Radius of small circle = 4 cm; radius of large circle = 7 cm

Radius of small circle = 4 cm; radius of large circle = 14 cm

Radius of small circle = 7 cm; radius of large circle = 8 cm

Radius of small circle = 8 cm; radius of large circle = 14 cm

Radius of small circle = 14 cm; radius of large circle = 16 cm

The diagrams below show constructions for two congruent triangles. What is the radius of each circle in the diagram on the right?

Mark a centre point, and use compasses to draw a circle.

Use a ruler to draw the diameter, AB, of circle.

Put compass needle at B and draw a 2nd circle.

Label one point where circles intersect C, and draw lines AC and BC.

Starting with the first step, put these instructions in the correct order to construct the triangle ABC where the hypotenuse, AB, is 5 cm and BC is 3 cm.

What equipment should you use to make an accurate construction of this triangle?

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

Laura is using GeoGebra to accurately draw a triangle with ∠BAC = 135° and ∠ABC = 32° and side AB = 6 units. Which of these tools should Laura use to draw side BC?

Use a protractor to measure 37° from A and mark a faint point.

Repeat the last step with point B and an angle of 40°.

Draw a ray line to show direction of side AC.

Draw a second ray line to show direction of side BC.

Label point C at the point where the two rays meet.

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

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

Lesson outcome