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Angles in Parallel Lines

Angles in Parallel Lines

What are the rules of 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 shown 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 shown 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. Allied (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 can be referred to as both allied or co-interior angles, either option is fine to use
    • You may also have heard these referred to as ‘C angles’ – do not use that term on an exam or you will lose marks!

How do I use the rules of angles in parallel lines?

  • Identify any matching angles and any angles that add up to 180°
  • STEP 1:
    Identify where the parallel lines are on the diagram
    • They will be marked with arrows or will be in a 2D shape that contains parallel lines
    • You may need to identify them from other reasons, such as vectors
  • STEP 2:
    Identify the  transverse
    • This is the straight line that extends across both parallel lines
  • STEP 3
    Use the information given in the question and the rules above to identify any one of the angles created at the intersection of the transverse and the parallel lines
    • For each transverse crossing one pair of parallel lines there will be four pairs of equal angles
    • Each pair will add up to 180°
  • STEP 4
    Fill in all the angles until you find the one you need
    • Once you have found the first angle,  x°, the others will either also be  x° or they will be 180° –  x°

NVNpCBEE_3-2-3-cie-igcse-angles-in-parallel-lines-diagram

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
    • You must give the correct name, F-angles, Z-angles and C-angles will NOT be awarded any marks on the exam

Worked example

Find the size of angles a and  b in the diagram below.

Give a reason for each step in your working.

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

Vertically opposite angles are equal.
Corresponding angles on parallel lines are equal.

You must write down  both of these reasons for full marks.

a = 64° (Vertically opposite angles are equal)
b = 64° (Corresponding angles on parallel lines are equal)

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