Scalene triangles have three different-sized angles and three edges of different lengths.

Isosceles triangles have two equal-sized angles. Two of the edges are equal in length.

Equilateral triangles have three equal-sized angles and three edges of equal length. They are regular triangles.

The radius is any line segment that joins the centre of a circle to any point on its circumference.

Constructing triangles

Maths

Checking compass skills

Securing the skill of using a pair of compasses

Understanding constructing a circle

Constructing rhombi

Diagonals of a rhombus

Bisecting an angle

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

Triangle PQR, where PQ  = 7 cm, PR = 12 cm and QR = 14 cm

Triangle PQR, where PQ  = 7 cm, PR = 14 cm and QR = 12 cm

Triangle PQR, where PQ  = 12 cm, PR = 14 cm and QR = 7 cm

Triangle PQR, where PQ  = 14 cm, PR = 7 cm and QR = 12 cm

Triangle PQR, where PQ  = 14 cm, PR = 12 cm and QR = 7 cm

When constructing a triangle from three edge lengths, we use a pair of compasses to draw {{ }} circles.

Which of the following shows a partial construction of an equilateral triangle?

Which of the following lengths could be the edge lengths of a triangle?

Which of the points C, D or E when connected to AB would create a triangle with three edges of different lengths?

Match the angle size to the type of angle.

Which of these sketched triangles are definitely isosceles?

Lucas has used a centimetre ruler to draw a line of 8.2 cm. Which image shows his line?

Which of these shows the best set up of a pair of compasses?

An arc of a circle is part of the circle’s {{ }}. 

A triangle has a perimeter of 65 mm. Two of the edges are 23 mm and 26 mm respectively. How long is the third edge of the triangle?

Constructing triangles

Lesson outcome