Parallel lines
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Explainer Video
Summary
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.
Definition
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.
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.
| NAME | INFORMAL NAME | DIAGRAM | RULE | |
| Alternate angles | Z-angles |  | Alternate angles are equal | |
| Interior angles | C-angles |
| Interior angles add up to | |
| Corresponding angles | F-angles |  | 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.
Example
In the diagram below, the lines and are parallel, as are the lines and . If , find the values of and .
Identify any angle pairs that form a rule.
Angles and are F-angles. So, they must be equal.
, as they are corresponding angles.
Angles and are Z-angles. So, they also must be equal.
, as they are alternate angles.
Angles and are angles on a straight line. So, they must add up to .
, as they are angles on a straight line.
FAQs - Frequently Asked Questions
How many types of angle pairs are there in parallel lines?
There are 3 types of angle pairs: alternate, interior and corresponding.
What are vertically opposite angles?
Vertically opposite angles are opposite angles formed by two intersecting lines.
What are parallel lines?
Parallel lines are lines that never meet.