4.2: Transversals
This activity is intended to supplement Geometry, Chapter 3, Lesson 3.
Problem 1 - Properties of Transversals
Use the below on the right to answer the following questions.
1. and is a pair of alternate interior angles
and is another pair
2. and is a pair of same-side interior angles
and is another pair
3. and is a pair of corresponding angles
and is another pair
Run the Cabri Jr. App and open the file TRNSVRSL showing two parallel lines, , cut by a transversal .
4. The measure of and are given.
a. These two angles are ____________________ Angles.
b. Move point to four different positions and record your measurements in the table.
position | position | position | position | |
---|---|---|---|---|
c. What is the relationship between the measurements of and ?
Congruent, complementary, or supplementary? _______________
5. The measure of and are given.
a. These two angles are ____________________ Angles.
b. Move point to four different positions and record your measurements in the table.
position | position | position | position | |
---|---|---|---|---|
c. What is the relationship between the measurements of and ?
Congruent, complementary, or supplementary? _______________
6. The measure of and are given.
a. These two angles are ____________________ Angles.
b. Move point to four different positions and record your measurements in the table.
position | position | position | position | |
---|---|---|---|---|
c. What is the relationship between the measurements of and ?
Congruent, complementary, or supplementary? _____________________
Problem 2 - Conjectures and Questions
Complete the following conjectures based on your answers above.
7. For parallel lines and a transversal, if two angles are corresponding angles, then...
8. For parallel lines and a transversal, if two angles are alternate interior angles, then...
9. For parallel lines and a transversal, if two angles are same-side interior angles, then...
Complete the following problems.
The triangles in the middle of the lines tell us that the lines are parallel.
10. Find the measurement of , , and .
11. Find the value of and .