# GCSE Mathematics – Revision Notes Topic ‘Geometry and Algebra’

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Contents

8. Points, Lines and Angles and Triangles 40

12. Triangles inside circles 60

# 1 Proportionality

Proportionality describes the relationship between two variables where the relationship between the two variables can be expressed in terms of a* proportionality constant*.

**Direct proportionality**

The variable* y* is said to be ** directly proportional **to the variable

*x*if their relationship can be described as

*y=cx*

where c is a constant.

The above can be re-written as , i.e. the **ratio** *y/x* is constant.

Direct proportionality can be observed when plotting *y* against * x*.

As *x* increases *y* increases.

The rate of the increase is the proportionality constant, 3.

**Inverse proportionality**

The variable *y* is said to be ** inversely proportional** to the variable

*x*if their relationship can be described as

This can be written as *yx = c*, i.e. the **product** *yx* is constant.

If *y* is inversely proportional to *x* then *y* decreases as *x* increases.

**Proportion to powers **

Direct and inverse proportionality can also be to the powers of *x*.

For example we could write:

*y* is directly proportional to x

*y* is directly proportional to

*y* is directly proportional to

*y* is directly proportional to

and

*y* is inversely proportional to x

*y* is inversely ...