Teach GCSE Maths

Constructing Triangles SAS, Constructing Triangles SAS, RHSRHS

Teach GCSE Maths

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Triangles Triangles SAS, RHSSAS, RHS

© Christine Crisp

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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.

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

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

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.

.

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

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.

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.

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.

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