To bisect means to cut or divide an object into two equal parts.

Complementary angles are a pair of angles that sum to 90°.

Supplementary angles are a pair of angles that sum to 180°.

Conjugate angles are a pair of angles that sum to 360°.

Constructing angles of  90° and 45°

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

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

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

The diagram shows the perpendicular to UV that passes through the point T. The perpendicular intersects UV at point S. Which of these constructions will produce a 45° angle?

EC is a perpendicular to BD. The angle BOE is bisected. Match each angle to its size.

An extension of AB in the direction of B.

The line segments AB and BC form an angle of 110°. Which of these constructions creates a 55° angle?

Line segments AB and BC are the legs of a 124° 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 124° angle. The diagram shows the two constructions that are applied to ABC. The angle $$z$$° is {{ }}°.

Andeep constructs the bisector of an angle of 104°. Andeep has made angles of {{}}°.

The diagram shows two congruent isosceles triangles put together to form a rhombus. Match each angle to its size.

Set your compasses to a width equal to the shorter of the two legs.

Place your compass needle on the vertex of the angle.

Make an arc on each leg, then place the compass needle on one arc.

Place the pencil on the vertex of the angle. Draw a circle.

Repeat on the open endpoint of the other leg.

Draw lines with a ruler to connect the points to form a rhombus.

Here are the steps to construct a rhombus given the legs of an angle. Match each step to the correct instruction.

Jacob wants to construct a rhombus using an angle with leg lengths of 10 cm and 15 cm. The maximum radius of each circle in the construction of this rhombus is {{ }} cm.

Lucas begins construction of a rhombus from this angle. Which point is the final vertex of the rhombus?

Jun is constructing an angle bisector. Here are the construction marks. Which two arcs did Jun draw first?

Constructing angles of 90° and 45°

Lesson outcome