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Working with Geometry Lines Study Guide

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Updated on Oct 5, 2011

Introduction to Working with Geometry Lines

Lesson Summary

This lesson introduces you to perpendicular, transversal, parallel, and skew lines. The angles formed by a pair of parallel lines and a transversal are also explained.

Both intersecting and nonintersecting lines surround you, but you may not pay much attention to them most of the time. In this lesson, you will focus on two different types of intersecting lines: transversals and perpendicular lines. You will also study nonintersecting lines: parallel and skew lines. You will learn about properties of lines that have many applications to this lesson and throughout this book. You'll soon start to look at the lines around you with a different point of view.

Intersecting Lines

On a piece of scratch paper, draw two straight lines that cross. Can you make these straight lines cross at more than one point? No, you can't, because intersecting lines cross at only one point (unless they are the same line). The point where they cross is called a point of intersection. They actually share this point, because it is on both lines. Two special types of intersecting lines are called transversals and perpendicular lines.

Transversals

A transversal is a line that intersects two or more other lines, each at a different point. In the following figure, line t is a transversal; line s is not.

Transversals

The prefix trans means across. In the previous figure, you can see that line t cuts across the two lines m and n. Line m is a transversal for lines s and t. Also, line n is a transversal across lines s and t. Line s crosses lines m and n at the same point (their point of intersection); therefore, line s is not a transversal. A transversal can cut across parallel as well as intersecting lines, as shown here:

Transversals

Perpendicular Lines

Perpendicular lines are another type of intersecting lines. Everyday examples of perpendicular lines include the horizontal and vertical lines of a plaid fabric and the lines formed by panes in a window. Perpendicular lines meet to form right angles. Right angles always measure 90°. In the following figure, lines x and y are perpendicular:

Perpendicular lines

The symbol "" means perpendicular. You could write x y to show these lines are perpendicular. Also, the symbol that makes a square in the corner where lines x and y meet indicates a right angle. In geometry, you shouldn't assume anything without being told. Never assume a pair of lines are perpendicular without one of these symbols. A transversal can be perpendicular to a pair of lines, but it does not have to be. In the following figure, line t is perpendicular to both line l and line m.

Perpendicular lines

Nonintersecting Lines

If lines do not intersect, then they are either parallel or skew.

Nonintersecting Lines

The symbol "" means parallel. So you can abbreviate the sentence, "Lines l and m are parallel," by writing "l m."Do not assume a pair of lines are parallel unless it is indicated. Arrowheads on the lines in a figure indicate that the lines are parallel. Sometimes, double arrowheads are necessary to differentiate two sets of parallel lines, as shown in the following figure:

Nonintersecting Lines

Everyday examples of parallel lines include rows of crops on a farm and railroad tracks. An example of skew lines is the vapor trails of a northbound jet and a westbound jet flying at different altitudes. One jet would pass over the other, but their paths would not cross.

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