# 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.

$\alpha=\gamma,\beta=\delta$

## 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 $180\degree$ |

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 $m$ and $n$ are parallel, as are the lines $r$ and $s$. If $a=70\degree$, find the values of $e,c$ and $d$*.

*Identify any angle pairs that form a rule.*

*Angles $a$ and $e$ are F-angles. So, they must be equal.*

$e=a=70\degree$, *as they are corresponding angles.*

*Angles $e$ and $c$ are Z-angles. So, they also must be equal.*

$c=e=70\degree$, *as they are alternate angles.*

*Angles $d$ and $c$ are angles on a straight line. So, they must add up to $180\degree$.*

$d=180-c=180-70=110\degree$, *as they are angles on a straight line.*

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