Teach GCSE Maths Constructing Triangles SAS, RHS.
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Transcript of Teach GCSE Maths Constructing Triangles SAS, RHS.
![Page 1: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/1.jpg)
Teach GCSE Maths
Constructing Triangles SAS, Constructing Triangles SAS, RHSRHS
![Page 2: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/2.jpg)
Teach GCSE Maths
ConstructiConstructing ng
Triangles Triangles SAS, RHSSAS, RHS
© 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"
![Page 3: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/3.jpg)
We are going to construct triangles when given 2 sides and 1 angle.
To do the exercises in this presentation you will need a ruler, compasses and protractor.
![Page 4: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/4.jpg)
8 cm B
C
A60
7cm
.
e.g. Construct triangle ABC with AB = 8
cm, AC = 7 cm and A = 60.
We draw the angle next so that we know where to draw AC.
We can only join BC in one way.
For this construction, the angle given is between the given sides. We call it SAS.
Using a ruler or compasses make AC = 7 cm.
x
![Page 5: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/5.jpg)
We can draw the triangle any way round. e.g.
They are all the same size and shape.
8cm B
C
A60
7cm
AB8cm
7cm
60
C
C
A
7cm
B60
8cm
![Page 6: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/6.jpg)
A
e.g. Construct triangle ABC with AB = 8
cm, BC = 10 cm and A = 90.
8cm B
C
10cm
If we are given 2 sides and a right angle we can also draw one triangle. It doesn’t matter which 2 sides we have.
We were given the right angle, the hypotenuse and another side, so we call this construction RHS.
.
![Page 7: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/7.jpg)
SUMMARY
e.g. 8cm60
7cm
Tip: We remember this as SAS ( the angle is between the 2 sides )
If we are given 2 sides and 1 angle, we can draw one triangle if the given sides form the given angle.
continued
![Page 8: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/8.jpg)
SUMMARY
Tip: If the sides don’t form the right angle, one side will be the hypotenuse so we remember this as RHS ( right angle, hypotenuse and side ).
8cmB
C
10cm
Ae.g.
If we are given 2 sides and a right angle, we can always draw 1 triangle.
![Page 9: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/9.jpg)
EXERCISE
1. Using a ruler and protractor, construct a triangle XYZ with XY = 10cm, X = 40 and XZ = 7cm. Measure YZ.
2. Using a ruler and protractor, construct a triangle PQR with PQ = 7cm, P = 90 and QR = 9cm. Measure PR and say why there is only 1 triangle.
All construction lines must be clearly shown.
![Page 10: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/10.jpg)
EXERCISE
Solution:
10cmY
Z
.40
7cm
X
YZ = 6·5 cm
1. Using a ruler and protractor, construct a triangle XYZ with XY = 10cm, X = 40 and XZ = 7cm. Measure YZ.
All of you will have drawn the same triangle.
![Page 11: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/11.jpg)
9cm
Solution:
Q
R
P 7cm
.
PR = 5·7cm
This is an example of RHS.
2. Using a ruler and protractor, construct a triangle PQR with PQ = 7cm, P = 90 and QR = 9cm. Measure PR.
Everyone’s triangle will be the same size and shape.
EXERCISE
![Page 12: Teach GCSE Maths Constructing Triangles SAS, RHS.](https://reader035.fdocuments.in/reader035/viewer/2022062722/56649f2f5503460f94c49872/html5/thumbnails/12.jpg)