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

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.

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?

This lesson will be removed by end of Summer Term 2025.

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

Lesson outcome

This lesson will be removed by end of Summer Term 2025.