**Parallel** lines room two or an ext lines the lie in the same aircraft and never intersect. To display that lines are parallel, arrows room used.

You are watching: Planes q and r are parallel. explain how you know lines a and b are skew.

*Label It*

*Say It*\(\overleftrightarrowAB \parallel \overleftrightarrowMN\) | Line \(AB\) is parallel to line \(MN\) |

\(l\parallel m\) | Line \(l\) is parallel to line \(m\). |

In the meaning of parallel words “line” is used. However, line segments, rays and planes can additionally be parallel. The image listed below shows 2 parallel planes, with a 3rd blue airplane that is perpendicular to both that them.

Figure \(\PageIndex2\)**Skew** lines space lines that room in different planes and also never intersect. They are different from **parallel lines** since parallel currently lie in the same plane. In the cube below, \(\overlineAB\) and \(\overlineFH\) room skew and \(\overlineAC\) and \(\overlineEF\) room skew.

then

Figure \(\PageIndex5\)Postulate: For any type of line and also a point ** not** ~ above the line, over there is one heat parallel come this line v the point. There space infinitely countless lines that go through \(A\), however only

**that is parallel come \(l\).**

*one*A **transversal** is a line the intersects two various other lines. The area *between* \(l\) and also \(m\) is the *interior*. The area *outside* \(l\) and also \(m\) is the *exterior*.

Example \(\PageIndex2\)

For \(\overlineXY\), how numerous parallel lines would pass through suggest \(D\)? surname this/these line(s).

**Solution**

One line, \(\overlineCD\)

Example \(\PageIndex3\)

True or false: some pairs of skew lines are also parallel.

**Solution**

This is false, by definition skew lines room in **different** planes and also parallel lines are in the **same** plane. Two lines could be skew or parallel (or neither), yet never both.

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Example \(\PageIndex4\)

Using the cube below, perform a pair of parallel lines.

## Review (Answers)

To check out the evaluation answers, open up this PDF record and watch for section 3.1.