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

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

Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

Applying constructions to loci problems

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

Constructing loci

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

Which diagram shows a perpendicular bisector?

Alex places two cones, A and B, on the ground. Which of these points are equidistant from A and B?

Which of these points are closer to TU than they are to ST?

Jacob wants to find all the points that are the same distance from LM as they are from MN. What construction should he use?

The region of points that are closer to A than to B.

The region of points that are closer to B than to A.

The region of points that are equidistant from A and B or closer to A than to B.

The region of points that are equidistant from A and B or closer to B than to B.

Which region is illustrated on this diagram?

Select the region which matches this description: closer to AB than BC and closer to CD than AD .

A __________ is a set of points that satisfy a given set of conditions.

Which diagram shows the locus of points 3 metres or less from point A?

Which diagram shows the locus of points more than 3 metres from point A?

Which diagram shows the locus of points 6 cm from the line segment AB?

Which diagram shows the locus of points less than 6 cm from the line segment AB?

Alex stands somewhere in his garden. Alex is less than 5 m from the house and more than 6 m from the tap. He is within 3 m of the tree. Alex is standing in region {{}}.

Applying constructions to loci problems

Lesson outcome