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# 4.2: Transversals

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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. $\angle{3}$ and $\angle{6}$ is a pair of alternate interior angles

$\angle \underline{\;\;\;\;\;\;\;}$ and $\angle \underline{\;\;\;\;\;\;\;}$ is another pair

2. $\angle{3}$ and $\angle{5}$ is a pair of same-side interior angles

$\angle \underline{\;\;\;\;\;\;\;}$ and $\angle \underline{\;\;\;\;\;\;\;}$ is another pair

3. $\angle{3}$ and $\angle{7}$ is a pair of corresponding angles

$\angle \underline{\;\;\;\;\;\;\;}$ and $\angle \underline{\;\;\;\;\;\;\;}$ is another pair

Run the Cabri Jr. App and open the file TRNSVRSL showing two parallel lines, $\overleftrightarrow{AD}\|\overleftrightarrow{HE}$, cut by a transversal $\overleftrightarrow{CG}$.

4. The measure of $\angle{ABC}$ and $\angle{HFB}$ are given.

a. These two angles are ____________________ Angles.

b. Move point $G$ to four different positions and record your measurements in the table.

$1^{st}$ position $2^{nd}$ position $3^{rd}$ position $4^{th}$ position
$m\angle{ABC}$
$m\angle{HFB}$

c. What is the relationship between the measurements of $\angle{ABC}$ and $\angle{HFB}$?

Congruent, complementary, or supplementary? _______________

5. The measure of $\angle{ABF}$ and $\angle{HFB}$ are given.

a. These two angles are ____________________ Angles.

b. Move point $G$ to four different positions and record your measurements in the table.

$1^{st}$ position $2^{nd}$ position $3^{rd}$ position $4^{th}$ position
$m\angle{ABF}$
$m\angle{HFB}$

c. What is the relationship between the measurements of $\angle{ABF}$ and $\angle{HFB}$?

Congruent, complementary, or supplementary? _______________

6. The measure of $\angle{DBF}$ and $\angle{HFB}$ are given.

a. These two angles are ____________________ Angles.

b. Move point $G$ to four different positions and record your measurements in the table.

$1^{st}$ position $2^{nd}$ position $3^{rd}$ position $4^{th}$ position
$m\angle{DBF}$
$m\angle{HFB}$

c. What is the relationship between the measurements of $\angle{DBF}$ and $\angle{HFB}$?

Congruent, complementary, or supplementary? _____________________

## Problem 2 - Conjectures and Questions

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 $\angle{1}$, $\angle{2}$, and $\angle{3}$.

11. Find the value of $x$ and $y$.

Feb 23, 2012

Aug 19, 2014