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 an angle not between them

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

Constructing loci

Applying constructions to loci problems

Solving loci problems in context

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

Finding all possible positions for a vertex when drawing a 2nd side

Drawing an angle to show what direction a side takes

Match the tools with what they are useful for when constructing a triangle.

Match each triangle to the type of triangle it is.

Alex makes an accurate drawing of the triangle in the sketch. Which point should Alex join Q to?

The following information is given for five different triangles. Alex and Sam both accurately construct each triangle. Which triangle information will definitely produce 2 congruent triangles?

Set compasses to 6 cm and draw a circle centre Q.

Mark R at the point(s) where the ray and circle meet.

Add the line(s) RQ to complete the triangle(s).

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

A pair of compasses is a tool which can be used to draw __________ and __________.

To create a right-angle you can construct a {{}} bisector.

Alex is constructing a right-angled triangle and has drawn a line segment. Which tool can be used to construct the perpendicular bisector of his line?

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

Radius of small circle = 3 cm; radius of large circle = 5 cm

Radius of small circle = 3 cm; radius of large circle = 10 cm

Radius of small circle = 5 cm; radius of large circle = 6 cm

Radius of small circle = 3 cm; radius of large circle = 6 cm

Radius of small circle = 6 cm; radius of large circle = 10 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 the circle.

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

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

Match each step to the correct instruction in order to construct the triangle ABC where the hypotenuse, AB, is 13 cm and BC is 5 cm.

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

Lesson outcome