Teach GCSE Maths

Constructing Triangles SSS

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Teach GCSE Maths

ConstructiConstructing ng

Triangles Triangles SSSSSS

© Christine Crisp

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To do the exercises in this presentation you will need a ruler, compasses and protractor.

We are going to draw some triangles as accurately as possible.

You need to be able to draw and measure lines accurate to 1 mm. and angles accurate to

1 degree.

Can you see a problem with now drawing AC ?

Ans: We don’t know what angle AC makes with AB.

Let’s start with AB. A B6cm

Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?

We have the same problem if we try to draw BC.

Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?

Let’s start with AB. A B

AC could be here . . .or here . . .

or here . . .

We need C to be in the position that makes BC = 5 cm.

CC

C C

To draw the triangle accurately we always use compasses and draw arcs from A and B.

6cm

4cm5cm

4 cm

4 cm4 cm

arc, radius 4

cm, centred at A

arc, radius 5

cm, centred at B

There is only one possible triangle.

Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?

A B

C

6cm

5cm

We must always show construction lines clearly.

4cm

An accurate drawing is often called a construction.

5cm 4cm

6cm

There is only one size and shape of triangle we can draw if we are given the lengths of 3 sides.

It doesn’t matter which way up, or which side we start with, all the triangles are congruent.

4cm 5cm

6cm

4cm5cm

6cm

4cm 5cm

6cm4cm

5cm

6cm

Tip: We can remember this as SSS ( 3 sides ).

4cm5cm

6cm

4cm 5cm

6cm

A B

Decide with your partner how to complete the triangle.Ans: We can use compasses opened to the

length AB and draw arcs at A and B which will meet at C.

If we are given one side of an equilateral triangle we can construct the triangle using compasses and a straight edge instead of a ruler .e.g. Complete the equilateral triangle ABC that

has AB as one side.

C

Now join AC and BC.

arc, radius AB, centred at A

arc, radius AB, centred at B

e.g. Construct a triangle with sides of lengths 6 cm, 4 cm and 5 cm.

SUMMARY

The triangle can be drawn accurately with a ruler and compasses.

An accurate drawing cannot be made without compasses.

A B6cm

4cm 5cm

Carc, radius 4

cm, centred at A

arc, radius 5

cm, centred at B

Only 1 shape and size of triangle can be drawn if we are given the lengths of 3 sides (SSS).

cont.

A Be.g.

We can construct an equilateral triangle ABC, if AB is already drawn, using only a straight edge and compasses.

If a side of the triangle is not drawn for us, we need a ruler to draw the 1st side.

SUMMARY

C

arcs of radius AB, centred at A and B.

EXERCISE

1. Using a ruler and compasses only, constructa triangle PQR with sides PQ = 8cm, PR = 6cm and QR = 6cm.Measure angles Q and R.

P Q

R

8cm

6cm 6cm Q = 48

R = 84

Solution:All construction lines must be clearly

shown.

EXERCISE2(a)Using a ruler and compasses only,

constructan equilateral triangle with sides of

length 7 cm.(b) Measure the angles with a protractor.

P Q

R

7cm

7cm 7cm

Solution:

60

60 60

If you have been accurate, all the angles will be 60.

All construction lines must be clearly shown.