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 constructing a perpendicular to a given line through a point

Maths

Checking and securing understanding of constructing the perpendicular bisector of a line segment

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

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 perpendicular to the line AB is a line that is at an angle of {{ }}° to AB.

The circle only touches the line segment LM once.

Sam hasn’t drawn all the expected construction arcs.

The line through P may not be perpendicular to LM.

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

Sam has incorrectly constructed a perpendicular for LM through P.  What is wrong with Sam's construction?

Which of these circles will help in the construction of the perpendicular to AB through point P.

Jun has partially completed a construction for a perpendicular of QR through P. What is incorrect about Jun’s pair of compasses?

The diagram shows the perpendicular through Z to the line segment SR. The shortest distance from Z to an extension of line segment SR 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.

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

Which of these is not a property of any rhombus? 

Two triangles are put together to form a quadrilateral. Which quadrilateral is a rhombus?

Aisha correctly draws three of the four arcs needed to construct the perpendicular bisector of LM. Point A is 6 cm away from point L. Point B is {{ }} cm away from point M.

Lucas correctly draws three of the four arcs needed to construct the perpendicular bisector of AB. Point C is {{}} from A and B.

Which of these diagrams show an accurate construction of a perpendicular bisector of the line segment PQ?

Checking and securing understanding of constructing a perpendicular to a given line through a point

Lesson outcome