Teach GCSE Maths Constructing Triangles SSS. If you have not done so, please see the file named...
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Transcript of Teach GCSE Maths Constructing Triangles SSS. If you have not done so, please see the file named...
Teach GCSE Maths
Constructing Triangles SSS
If you have not done so, please see the file named Sample Pages before viewing this
presentation.
Teach GCSE Maths
ConstructiConstructing ng
Triangles Triangles SSSSSS
© Christine Crisp
"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"
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.