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 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
- 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 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 and select Open.
By moving point , 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 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. and is another pair
2. and is another pair
3. and is another pair
4. a. Corresponding
b. Sample measurements.
position | position | position | position | |
---|---|---|---|---|
109 | 84 | 56 | 37 | |
109 | 84 | 56 | 37 |
c. Congruent
5. a. Same-Side Interior
b. Sample measurements.
position | position | position | position | |
---|---|---|---|---|
150 | 136 | 112 | 75 | |
30 | 44 | 68 | 105 |
c. Supplementary
6. a. Alternate Interior
b. Sample measurements.
position | position | position | position | |
---|---|---|---|---|
43 | 60 | 108 | 125 | |
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. , , and are all equal to
11.