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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.

## Problem 1 - Properties of Transversals

Use the below on the right to answer the following questions.

1. 3\begin{align*}\angle{3}\end{align*} and 6\begin{align*}\angle{6}\end{align*} is a pair of alternate interior angles

\begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} and \begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} is another pair

2. 3\begin{align*}\angle{3}\end{align*} and 5\begin{align*}\angle{5}\end{align*} is a pair of same-side interior angles

\begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} and \begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} is another pair

3. 3\begin{align*}\angle{3}\end{align*} and 7\begin{align*}\angle{7}\end{align*} is a pair of corresponding angles

\begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} and \begin{align*}\angle \underline{\;\;\;\;\;\;\;}\end{align*} is another pair

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

4. The measure of ABC\begin{align*}\angle{ABC}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*} are given.

a. These two angles are ____________________ Angles.

b. Move point G\begin{align*}G\end{align*} to four different positions and record your measurements in the table.

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*}
mHFB\begin{align*}m\angle{HFB}\end{align*}

c. What is the relationship between the measurements of ABC\begin{align*}\angle{ABC}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*}?

Congruent, complementary, or supplementary? _______________

5. The measure of ABF\begin{align*}\angle{ABF}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*} are given.

a. These two angles are ____________________ Angles.

b. Move point G\begin{align*}G\end{align*} to four different positions and record your measurements in the table.

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*}
mHFB\begin{align*}m\angle{HFB}\end{align*}

c. What is the relationship between the measurements of ABF\begin{align*}\angle{ABF}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*}?

Congruent, complementary, or supplementary? _______________

6. The measure of DBF\begin{align*}\angle{DBF}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*} are given.

a. These two angles are ____________________ Angles.

b. Move point G\begin{align*}G\end{align*} to four different positions and record your measurements in the table.

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*}
mHFB\begin{align*}m\angle{HFB}\end{align*}

c. What is the relationship between the measurements of DBF\begin{align*}\angle{DBF}\end{align*} and HFB\begin{align*}\angle{HFB}\end{align*}?

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 1\begin{align*}\angle{1}\end{align*}, 2\begin{align*}\angle{2}\end{align*}, and 3\begin{align*}\angle{3}\end{align*}.

11. Find the value of \begin{align*}x\end{align*} and \begin{align*}y\end{align*}.

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