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.

Bisecting an angle

Maths

Checking compass skills

Securing the skill of using a pair of compasses

Understanding constructing a circle

Constructing triangles

Constructing rhombi

Diagonals of a rhombus

Perpendicular bisector of a line segment

Perpendicular to a given line through a given point

Problem solving with constructions

The constructions covered in this unit are built on in the future unit. In the future unit, pupils construct triangles and construct diagrams following specific restrictions.

The prior unit gave pupils the opportunity to explore polygons and begin to generalise their understanding of interior/exterior angles in regular polygons. In this unit, pupils will use the geometrical properties of a rhombus to perform various constructions. 

In this unit we develop skills in using a pair of compasses and ruler to construct various accurate shapes and angles including triangles, rhombi, perpendicular lines and angle bisectors.

Constructions

Which of these diagrams shows the compass width being accurately set to 5 cm?

What is the value of $$r$$, the radius of the circle drawn?

A rhombus has been constructed as both legs of the angle are of equal length.

A rhombus has been constructed as both circles use endpoints A and B as centres.

A rhombus hasn't been constructed as all four sides aren't of equal length.

A rhombus hasn't been constructed as both circles are not the same size.

A rhombus hasn't been constructed as a pair of compasses haven't been used.

Which statements are correct about this construction?

The two legs of the angle are different in length. Which compass placement is correct in order to create a pair of shorter legs of equal length?

This diagram shows the correct constructions to bisect an angle. Which point of intersection between two circles must the bisecting line pass through?

Which of these construction arcs could be the first to be drawn in a construction to bisect an angle?

This quadrilateral is a rhombus. What is the size of angle $$x$$?

This quadrilateral is a rhombus. What is the size of angle $$r$$?

This quadrilateral is a rhombus. What is the perimeter of this rhombus (in cm)?

The rhombus has been split into two scalene triangles.

The rhombus has been split into two isosceles triangles.

The angle of 80° has been cut exactly in half.

The rhombus on the right is congruent to the rhombus on the left, with one diagonal drawn. Which of these statements correctly describes the rhombus after its diagonal has been drawn on?

Both rhombi are congruent, with the right-hand rhombus having both diagonals drawn on. Match the angles in the rhombus to its size.

Which of these quadrilaterals have the correct feathers, hash marks, and/or angle markers that confirm the shape is a rhombus?

Bisecting an angle

Lesson outcome