Maths GCSE

Overview of the Trangle part of the course. 

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Congruence

If one or more of these 4 conditions hold then the two triangles are congruent:

1. SSS - three sides are the same

2. AAS - two angles and a side match up

3. SAS - two sides and an angle match up

4. RHS - a right angle, the hypotenuse and one other side match up

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Scale Factor

For scale factor 'n' :

The sides are n times bigger

The areas are n squared times bigger

The volumes are n cubed times bigger 

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Example

2 spheres have surface areas of 16m squared and 25m squared. Find the ratio of their volumes.

Area = a squared : b squared = 16 : 25

Therefore...  a : b = 4 : 5

Therefore...  a cubed : b cubed = 64 :125

Volume of the spheres = 64m cubed and 125m cubed

        

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Transformations

How to remember the 4 transformations

'TERRY'

T = Translation

E = Enlargement

R = Rotation

R = Reflection

Y

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Translation

When an object is translated all that changes is the position of the object.

You must specify the vector of the translation.

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Enlargement

When an object is enlarged all that changes is the size (unless it is a negative scale factor because then the orientation changes also)

You must specify the scale factor and the centre of enlargement.

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Rotation

When an object is rotated all that changes is the position and orientation.

You must specify the angle turned, the direction turned and the centre of rotation.

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Reflection

When an object is reflected all that changes is the position and orientation.

You must specify the mirror line

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