Angles in Parallel Lines
What are parallel lines?
- Parallel lines are lines that are always equidistant (the same distance apart)
- No matter how far the lines are extended in either direction, they will never meet
- Angles are formed when a straight line cuts through two parallel lines
What are corresponding angles in parallel lines?
- Find corresponding angles by looking for an F-shape
- Corresponding angles are equal
What are alternate angles in parallel lines?
- Find alternate angles by looking for a Z-shape
- Alternate angles are equal
What are co-interior (supplementary) angles in parallel lines?
- Find co-interior angles by looking for a C-shape
- Co-interior angles add up to 180°
How do I find missing angles in parallel lines?
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Look for shapes that look like F, Z, or C
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Vertically opposite angles can also be used in problems involving parallel lines
- The below diagram shows how identifying angle x, can lead to knowing information about several other angles
- The green angle opposite is also x, as it is vertically opposite
- The orange angle must be 180-x as angles on a straight line sum to 180°
- The below diagram shows how identifying angle x, can lead to knowing information about several other angles
- You should also be able to spot corresponding angles, alternate angles, and co-interior angles in this diagram
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 use the correct names as listed above
- Do not use F, Z and C angles otherwise you will lose marks!
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)
