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

A rhombus is a parallelogram where all sides are the same length.

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

Checking and securing understanding of bisecting an angle

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

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 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

Aisha constructs the bisector of an angle of 72°. Aisha 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.

Place the compass needle on the arc of one leg created in the previous step.

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

Repeat on the open endpoint of the other leg.

Use a ruler to connect the points to form a rhombus.

Starting with the first step, put these steps in order to construct a rhombus given the legs of an angle.

Jun wants to construct a rhombus using an angle with leg lengths of 11 cm and 17 cm. The maximum radius of each circle in the construction of this rhombus is {{ }} cm.

Alex begins construction of a rhombus from this angle. The final vertex of the rhombus is at point {{}}.

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

A perpendicular bisector of the line PQ is a line that is at an angle of {{ }}° to PQ. It cuts PQ exactly in half.

The line segment PQ should touch the circle twice.

Izzy hasn’t drawn all the expected construction arcs.

It is only possible to draw a perpendicular through the midpoint of PQ.

The line through R may not be perpendicular to PQ.

Izzy has incorrectly constructed a perpendicular for PQ through R.  What is wrong with Izzy's construction?

Which of these circles does not help in the construction of the perpendicular to LM through point P?

Laura has partially completed a construction for a perpendicular of AB through O. What is incorrect about Laura’s pair of compasses?

The diagram shows the perpendicular through Z to the line segment SR. The radius of the circle is {{ }} cm.

The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to the original line segment SR is {{}} cm.

Starter Quiz

A perpendicular bisector of the line PQ is a line that is at an angle of ° to PQ. It cuts PQ exactly in half.