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# 4.1: Parallel Lines Cut By A Transversal

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Geometry, Chapter 3, Lesson 2.

## Problem 1 - Exploring Parallel Lines

In this activity, students will develop and strengthen their knowledge about the angles formed when parallel lines are cut by a transversal. The measurement tool helps them discover the relationships between and among the various angles in the figure. Students will draw parallel lines, draw a transversal, and explore angle relationships.

Press APPS. Move down to the CabriJr application and press ENTER. Press ENTER, or any key, to begin using the application.

Press Y=\begin{align*}Y=\end{align*} for the F1\begin{align*}F1\end{align*} menu and select New. (If asked to Save changes? press choose “No.”)

Press WINDOW for F2\begin{align*}F2\end{align*}, move to Line and press ENTER.

Move down and to the left and press ENTER to mark one point on the line. Move to the right and press ENTER to mark the second point defining the line.

Press ZOOM for F3\begin{align*}F3\end{align*}, move to Parallel, and press ENTER. Move the pencil until the line is blinking. Press ENTER then press \begin{align*}\uparrow\end{align*} until the second line is in the desired location. Press ENTER to mark the point through which the parallel line is drawn.

Press WINDOW for F2\begin{align*}F2\end{align*} and select Line. Move up and mark a point by pressing ENTER. Move down and left and press ENTER to mark the second point defining the transversal of the two parallel lines.

Now we will measure angles and explore angle relationships.

Press GRAPH for F5\begin{align*}F5\end{align*}. Move down to Measure, then right and down to Angle then press ENTER. You must select three points to identify the angle. Move the pencil until one of the lines is flashing and press ENTER to select a point on that line. Move the pencil until one of the parallel lines and the transversal are both flashing and press ENTER. This will mark their intersection as the vertex of the angle. Move the pencil to the other line forming a side of the angle. Press ENTER when that line is flashing. Move the measurement to a convenient location. Press CLEAR to turn off the hand.

With the angle measuring tool active, measure some of the other angles formed—corresponding, alternate interior, alternate exterior...

Move each measurement to a convenient location. Press CLEAR to turn off the hand

Move the pointer to one of the points which defined the location of the transversal. Press ALPHA to activate the hand and move this point. Observe the angle measures as the position of the transversal changes.

## Problem 2 - Extension

Move the transversal until one of the angles has “crossed over” and observe that you now have consecutive interior angles that are supplementary.

Measure the remaining angles and observe the relationships among the angle measures.

Load a background image of parallel lines but by a transversal with angles named. Instruct students to move their cursors to: the interior, the exterior, to an angle with a specific characteristic (congruent to a given angle, supplementary to a given angle, ...).

Press 2nd\begin{align*}2^{nd}\end{align*} MODE to exit the application.

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