Edexcel IGCSE Maths

Revision Notes

4.1.1 Angles in Parallel Lines

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 3 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!

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!

Exam Tip

Do not forget to give reasons for each step of your working in an angles question.

These are often needed to get full marks!

Worked Example

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

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