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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

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

11. Find the value of x and y.

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Date Created:

Feb 23, 2012

Last Modified:

Nov 03, 2014
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TI.MAT.ENG.SE.1.Geometry.4.2

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