Perpendicular bisector of a line segment

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

Bisecting an angle

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 show a perpendicular bisector on a rhombus?

Which of these compass widths are suitable when constructing the perpendicular bisector of the given line segment?

Which of these constructions can be used to draw on the perpendicular bisector of the line segment given?

7 cm away from Y and greater than 7 cm away from Z.

7 cm away from Y and less than 7 cm away from Z.

7 cm away from Z and greater than 7 cm away from Y.

Each of the two circles has been drawn with a radius of 7 cm, one with centre Y, and the other with centre Z. Match the statement to the point it describes.

Constructing arcs of radius 6 cm at both points R and S.

Constructing arcs of radius 9 cm at both points R and S.

Constructing arcs of radius 12 cm at both points R and S.

Constructing arcs of radius 18 cm at both points R and S.

Constructing an arc of radius 12 cm at R and an arc of radius 18 cm at S.

Lucas wants to construct the perpendicular bisector of line segment RS, which has a length of 18 cm. Which of these construction methods are possible?

A perpendicular bisector to YZ has definitely been constructed.

A perpendicular bisector to YZ has definitely not been constructed.

The construction of the perpendicular bisector to YZ is incomplete.

The angle between the two line segments is 88°.

Which of these statements is true about this construction?

This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$p$$?

This quadrilateral is a rhombus with one of its diagonals drawn on. What is the size of angle $$m$$?

This quadrilateral is a rhombus with both of its diagonals drawn on. Match the angles in the rhombus to its size.

A rhombus has side length of 41 cm, and diagonals of length 18 cm and 80 cm. What is the area of this rhombus (in cm²)?

This triangle is reflected with the line of reflection at its base side. The resultant quadrilateral is a rhombus. What is the area of this rhombus (in cm²)?

Perpendicular bisector of a line segment

Lesson outcome