Revision Notes

What are parallel lines?

Parallel lines are lines that are always equidistant (ie the same distance apart) – no matter how far the lines are extended in either direction, they will never meet.

Working with angles in parallel lines

There are three main rules:

1. Corresponding angles are equal
A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below:

Corresponding-Angles, IGCSE & GCSE Maths revision notes

(Note: You may also have heard these referred to as ‘F angles’ – do not use that term in an exam or you will lose marks!)

2. Alternate angles are equal
A line cutting across two parallel lines creates two pairs of equal alternate angles, as in the diagram below:

Alternate-Angles, IGCSE & GCSE Maths revision notes

(Note: You may also have heard these referred to as ‘Z angles’ – do not use that term on an exam or you will lose marks!)

3. Co-interior angles add to 180°
A line cutting across two parallel lines creates two pairs of co-interior angles.  In the diagram below, the two coloured angles on the left add up to 180°, as do the two coloured angles on the right:

Co-interior-Angles, IGCSE & GCSE Maths revision notes

(Note: These are sometimes referred to as allied angles, which is fine.  You may also have heard these referred to as ‘C angles’ – do not use that term on an exam or you will lose marks!)

And don’t forget the basics:

4. Vertically opposite angles are equal

Whenever two straight lines cross, they create two pairs of equal vertically opposite angles, as in the diagram below:

Opposite-Angles, IGCSE & GCSE Maths revision notes

Don’t forget this rule when answering parallel line questions!  For example, in the following diagram the highlighted angles are equal:

Opposite-Angles-in-context, IGCSE & GCSE Maths revision notes

(Note: vertically opposite angles are sometimes simply called opposite angles.  Either term will get you the marks.)

5. Angles on a line add to 180°

This rule is also still true with parallel line questions!  In the following diagram, for example, the highlighted angles add up to 180°:

Angles-on-a-Line-in-context, IGCSE & GCSE Maths revision notes

Then:

6. Just angle chase!

Example

Angles in Parallel Lines Example 64 degrees, IGCSE & GCSE Maths revision notes

Question

Edexcel GCSE Maths Notes

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