A locus is a set of points that satisfy a given set of conditions. Multiple sets of points are referred to as loci.

A circle is a locus of points that are equidistant from a fixed point. This fixed point is the centre of the circle and the distance from the centre to the locus of points is the radius of the circle.

Constructing loci

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

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 {{ }} is a set of points that satisfy a given set of conditions.

Which diagram shows the locus of points exactly 2 metres from point P?

Which diagram shows the locus of points less than 2 metres from point P?

Which diagram shows the locus of points 5 metres or more from the line segment PQ?

Which diagram shows the locus of points less than 5 metres from the line segment PQ?

Izzy stands somewhere in her garden. Izzy is less than 5 m from the house and less than 6 m from the tap. She is within 3 m of the tree. Izzy is standing in region {{}}.

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 B to?

The following information is given for five different triangles. Jun and Sam both accurately construct each triangle. Which triangle information may not produce 2 congruent triangles?

Set compasses to 7 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).

Match each step to the correct instruction in order to construct the triangle PQR.

Constructing loci

Lesson outcome