Parallel lines

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Parallel lines

​​In a nutshell

Parallel lines are lines that will never meet. Angles in parallel lines have their own set of rules you need to learn.


Two lines are parallel if they will never meet (or intersect). Parallel lines are lines that are moving in the exact same direction.

Representing parallel lines

A pair of parallel lines can be represented by matching arrowheads on both lines.

Vertically opposite angles

Two straight lines intersecting create two pairs of vertically opposite angles. What you need to know is that vertically opposite angles are equal in size.

Maths; Lines and angles; KS3 Year 7; Parallel lines


Alternate, interior and corresponding angles

When two parallel lines are intersected by a third line, pairs of angles can appear in three different forms. Each of these forms have their own rules.





Alternate angles


Maths; Lines and angles; KS3 Year 7; Parallel lines

Alternate angles are equal

Interior angles


Maths; Lines and angles; KS3 Year 7; Parallel lines

Interior angles add up to 180°180\degree​​

Corresponding angles


Maths; Lines and angles; KS3 Year 7; Parallel lines

Corresponding angles are equal

Note: The informal names are given to make it easier to identify and remember the rules. When solving questions, you must use the actual names of each type.

Angle problems

To solve problems involving angles in parallel lines, you need to be able to identify when you can use a rule that helps you find out more angles in the question.


In the diagram below, the lines mm and nn are parallel, as are the lines rr and ss. If a=70°a=70\degree, find the values of e,ce,c and dd.

Maths; Lines and angles; KS3 Year 7; Parallel lines

Identify any angle pairs that form a rule.

Angles aa and ee are F-angles. So, they must be equal.

e=a=70°e=a=70\degree​, as they are corresponding angles.

Angles ee and cc are Z-angles. So, they also must be equal.

c=e=70°c=e=70\degree​, as they are alternate angles.

Angles dd and cc are angles on a straight line. So, they must add up to 180°180\degree.

d=180c=18070=110°d=180-c=180-70=110\degree​, as they are angles on a straight line.

e=70°,c=70°,d=110°\underline{e=70\degree,c=70\degree, d = 110\degree}​​

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FAQs - Frequently Asked Questions

How many types of angle pairs are there in parallel lines?

What are vertically opposite angles?

What are parallel lines?


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