4.2: Transversals
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 sameside 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
 SameSide Interior angles are supplementary
Teacher Preparation and Notes
 This activity was written to be explored with Cabri Jr.
 To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
 To download the calculator file, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=10989 and select TRNSVRSL.8xv.
Associated Materials
 Student Worksheet: Transversals http://www.ck12.org/flexr/chapter/9688, scroll down to the second activity.
 Cabri Jr. Application
 TRNSVRSL.8xv
Exploring Parallel Lines cut by a Transversal
Before beginning the activity, students should know the definition of corresponding, alternate interior and sameside 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 \begin{align*}Y=\end{align*}
By moving point \begin{align*}G\end{align*}
For Questions 4, 5, and 6, students will move point \begin{align*}G\end{align*}
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. \begin{align*}\angle{4}\end{align*}
2. \begin{align*}\angle{4}\end{align*}
3. \begin{align*}\angle{4}\end{align*}
4. a. Corresponding
b. Sample measurements.
\begin{align*}1^{st}\end{align*} 
\begin{align*}2^{nd}\end{align*} 
\begin{align*}3^{rd}\end{align*} 
\begin{align*}4^{th}\end{align*} 


\begin{align*}m\angle{ABC}\end{align*} 
109  84  56  37 
\begin{align*}m\angle{HFB}\end{align*} 
109  84  56  37 
c. Congruent
5. a. SameSide Interior
b. Sample measurements.
\begin{align*}1^{st}\end{align*} 
\begin{align*}2^{nd}\end{align*} 
\begin{align*}3^{rd}\end{align*} 
\begin{align*}4^{th}\end{align*} 


\begin{align*}m\angle{ABF}\end{align*} 
150  136  112  75 
\begin{align*}m\angle{HFB}\end{align*} 
30  44  68  105 
c. Supplementary
6. a. Alternate Interior
b. Sample measurements.
\begin{align*}1^{st}\end{align*} 
\begin{align*}2^{nd}\end{align*} 
\begin{align*}3^{rd}\end{align*} 
\begin{align*}4^{th}\end{align*} 


\begin{align*}m\angle{DBF}\end{align*} 
43  60  108  125 
\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 sameside interior angles, then they are supplementary.
Extra Problems
10. \begin{align*}\angle{1}\end{align*}
11.
\begin{align*}108 & = 7x4 \quad \text{and}\quad y = 72 \\
112 & = 7x \\
16 & = x\end{align*}
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