1. Constructing Triangles SSS
Teach GCSE Maths
Constructing Triangles SSS

2. If you have not done so, please see the file named Sample Pages before viewing this presentation.

3. Constructing Triangles SSS
Teach GCSE Maths
Constructing Triangles SSS
"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"
© Christine Crisp

4. 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.

5. Can you see a problem with now drawing AC ?
Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?
Let’s start with AB. A B
6cm
Can you see a problem with now drawing AC ?
Ans: We don’t know what angle AC makes with AB.
We have the same problem if we try to draw BC.

6. We need C to be in the position that makes BC = 5 cm.
Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm?
Let’s start with AB. A B
6cm
AC could be here . . .
4 cm
4cm
5cm
or here . . .
4 cm C
4 cm
or here . . . C C C
arc, radius 4 cm, centred at A
arc, radius 5 cm, centred at B
We need C to be in the position that makes BC = 5 cm.
To draw the triangle accurately we always use compasses and draw arcs from A and B.
There is only one possible triangle.

7. An accurate drawing is often called a construction.
Could you draw a triangle ABC with sides AB = 6cm, AC = 4cm and BC = 5cm? A B
6cm
4cm
5cm C
An accurate drawing is often called a construction.
We must always show construction lines clearly.

8. Tip: We can remember this as SSS ( 3 sides ).
There is only one size and shape of triangle we can draw if we are given the lengths of 3 sides.
Tip: We can remember this as SSS ( 3 sides ).
It doesn’t matter which way up, or which side we start with, all the triangles are congruent.
4cm
5cm
6cm
4cm
5cm
6cm
5cm
4cm
6cm
4cm
5cm
6cm
4cm
5cm
6cm
4cm
5cm
6cm
4cm
5cm
6cm

9. 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. A B C
arc, radius AB, centred at A
arc, radius AB, centred at B
Ans: We can use compasses opened to the length AB and draw arcs at A and B which will meet at C.
Decide with your partner how to complete the triangle.
Now join AC and BC.

10. SUMMARY
Only 1 shape and size of triangle can be drawn if we are given the lengths of 3 sides (SSS).
The triangle can be drawn accurately with a ruler and compasses.
e.g. Construct a triangle with sides of lengths
6 cm, 4 cm and 5 cm. A B
6cm
4cm
5cm
arc, radius 4 cm, centred at A
arc, radius 5 cm, centred at B C
An accurate drawing cannot be made without compasses.
cont.

11. SUMMARY
We can construct an equilateral triangle ABC, if AB is already drawn, using only a straight edge and compasses. A B
e.g.
arcs of radius AB, centred at A and B. C
If a side of the triangle is not drawn for us, we need a ruler to draw the 1st side.

12. All construction lines must be clearly shown.
EXERCISE
Using a ruler and compasses only, construct
a triangle PQR with sides PQ = 8cm, PR = 6cm and QR = 6cm.
Measure angles Q and R.
Solution:
All construction lines must be clearly shown.
8cm P Q
6cm
6cm
Q = 48 
R = 84  R

13. All construction lines must be clearly shown.
EXERCISE
2(a) Using a ruler and compasses only, construct
an equilateral triangle with sides of length 7 cm.
(b) Measure the angles with a protractor.
Solution:
All construction lines must be clearly shown.
7cm P Q
60
60
7cm
7cm
If you have been accurate, all the angles will be 60.
60 R