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Syllabus Edition
First teaching 2021
Last exams 2024
Angles in Parallel Lines (CIE IGCSE Maths: Extended)
Revision Note
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.
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:
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- 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!
- 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:
- 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:
- Note: These are referred to as either allied or co-interior angles, either is fine to use in the exam
- 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°
Examiner 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 the angles a and b in the diagram below.
Give a reason for each step in your working.
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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