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# 4.2: Transversals

Difficulty Level: At Grade Created by: CK-12

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

ID: 10989

Time required: 15 minutes

## Activity Overview

In this activity, students will explore corresponding, alternate interior and same-side interior angles. This is an introductory activity where students will need to know how to grab points in Cabri Jr.

Topic: Points, Lines & Planes

• Corresponding angles are congruent
• Alternate Interior angles are congruent
• Same-Side Interior angles are supplementary

Teacher Preparation and Notes

Associated Materials

## Exploring Parallel Lines cut by a Transversal

Before beginning the activity, students should know the definition of corresponding, alternate interior and same-side interior angles. Questions 1, 2, and 3 ask students to name pairs of angles from the diagram. This should be done without the use of the calculator.

Students will now run the Cabri Jr. App and open the file TRNSVRSL. To open a file, they should press Y=\begin{align*}Y=\end{align*} and select Open.

By moving point G\begin{align*}G\end{align*}, students will discover the properties of two parallel lines cut by a transversal. To move a point, students need to move the cursor over the point (a square) and press ALPHA.

For Questions 4, 5, and 6, students will move point G\begin{align*}G\end{align*} to four different places. They should record the angle measurements in the tables on the worksheet. Then, students should try to generalize their results in the Conjecture section.

There are two application problems at the end of the worksheet for students to apply what they have learned in the activity. These problems can be done as homework.

## Solutions

1. 4\begin{align*}\angle{4}\end{align*} and 5\begin{align*}\angle{5}\end{align*} is another pair

2. 4\begin{align*}\angle{4}\end{align*} and 6\begin{align*}\angle{6}\end{align*} is another pair

3. 4\begin{align*}\angle{4}\end{align*} and 8\begin{align*}\angle{8}\end{align*} is another pair

4. a. Corresponding

b. Sample measurements.

1st\begin{align*}1^{st}\end{align*} position 2nd\begin{align*}2^{nd}\end{align*} position 3rd\begin{align*}3^{rd}\end{align*} position 4th\begin{align*}4^{th}\end{align*} position
mABC\begin{align*}m\angle{ABC}\end{align*} 109 84 56 37
mHFB\begin{align*}m\angle{HFB}\end{align*} 109 84 56 37

c. Congruent

5. a. Same-Side Interior

b. Sample measurements.

1st\begin{align*}1^{st}\end{align*} position 2nd\begin{align*}2^{nd}\end{align*} position 3rd\begin{align*}3^{rd}\end{align*} position 4th\begin{align*}4^{th}\end{align*} position
mABF\begin{align*}m\angle{ABF}\end{align*} 150 136 112 75
mHFB\begin{align*}m\angle{HFB}\end{align*} 30 44 68 105

c. Supplementary

6. a. Alternate Interior

b. Sample measurements.

1st\begin{align*}1^{st}\end{align*} position 2nd\begin{align*}2^{nd}\end{align*} position 3rd\begin{align*}3^{rd}\end{align*} position 4th\begin{align*}4^{th}\end{align*} position
mDBF\begin{align*}m\angle{DBF}\end{align*} 43 60 108 125
mBFH\begin{align*}m\angle{BFH}\end{align*} 43 60 108 125

c. Congruent

Conjectures

For parallel lines and a transversal…

7. if two angles are corresponding angles, then they are congruent.

8. if two angles are alternate interior angles, then they are congruent.

9. if two angles are same-side interior angles, then they are supplementary.

Extra Problems

10. 1\begin{align*}\angle{1}\end{align*}, 2\begin{align*}\angle{2}\end{align*}, and 3\begin{align*}\angle{3}\end{align*} are all equal to 55\begin{align*}55^\circ\end{align*}

11.

10811216=7x4andy=72=7x=x\begin{align*}108 & = 7x-4 \quad \text{and}\quad y = 72 \\ 112 & = 7x \\ 16 & = x\end{align*}

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