# Parallel and Perpendicular Lines

### Topics

## Introduction to :

*Parallel Lines* is Blondie's third album. Who's that? Seriously? Blondie was breaking hearts of glass way before Gaga got her blonde on.

The album cover is rockin' some stripes. Maybe that's where they got the title. Aside from the obvious influence that parallel lines have on everyone and everything, we mean.

**Parallel lines** are coplanar lines that never intersect. If pictures are overkill, you can use the symbol || to get the job done. So in the image above, we could say, "Line *DE* and line *PQ* are parallel," or we could just write *DE* || *PQ*. Of course, drawing the lines out is always an option too.

What about the other types of lines out there? Lines that lie on the same plane and *do* intersect are called **intersecting lines**. Really creative, we know. We'll talk about intersecting lines a little later, so don't get your panties in a bunch.

Lines that lie on different planes and never intersect are called **skew lines**. They aren't perfectly in sync like parallel lines but they don't clash like intersecting lines either. They kind of just go about their own business separately, never meeting or even acknowledging one another.

To show that lines are parallel in drawings, it's common to draw an arrowhead or two on the parallel lines. Just like tick marks are used to indicate congruent segments, these arrowheads clarify which line is parallel to which other line.

### Sample Problem

Which pairs of lines are parallel?

Well, we know that intersecting lines can't be parallel, so that means that lines *d* and *e* can't be parallel to *a*, *b*, or *c*. From the image, we can tell that *d* and *e* both have one arrowhead each, so they must be parallel to each other. Of *a*, *b*, and *c*, only *a* and *c* have double arrowheads, so that means they are parallel. Therefore *a* || *c* and *d* || *e*, but *b* isn't parallel to any of them.

#### Example 1

What is the defining characteristic of parallel lines? |

#### Example 2

What symbol do you use to indicate that |

#### Example 3

How do you indicate that |

#### Example 4

A line that goes through point (2, 2) is parallel to a line with an equation of 2 |

#### Exercise 1

Can two lines that intersect be parallel to each other?

#### Exercise 2

Can two lines that lie on the same plane be parallel to each other?

#### Exercise 3

Line *u* is parallel to line *l* and line *l* is parallel to line *i*. Is it true that line *u* is parallel to line *i*?

#### Exercise 4

Line *j* is parallel to line *k*. If line *j* has the equation *y* = 3*x* – 1, what slope must line *k* have?

#### Exercise 5

Line *p* is parallel to line *q*. If line *p* has the equation 4*x* + 5*y* = 15 and line *q* passes through point (5, 5), what is the equation of line *q*?