2.6 Special Angles on Parallel Lines

Topic:Angles, Geometry, Straight Lines, Mathematics

Investigation #1

Line AD is parallel to Line FG in the figure below. 1. Use the angle tool to measure all 8 angles in the figure below. 2. Click and drag point C to change the angle measures. 3. Complete the questions below the figure based on your observations.

Use this figure for Investigation #1

Observation

Which of the following statements is always true about corresponding pairs of angles, like and ?

Select all that apply

A
They are always complementary.
B
They are always supplementary.
C
They are always congruent.
D
They are not related.

Check my answer (3)

Which of the following statements is always true about alternate exterior pairs of angles, like and ?

Select all that apply

A
They are always complementary.
B
They are always supplementary.
C
They are always congruent.
D
They are not related.

Check my answer (3)

Which of the following statements is always true about alternate interior pairs of angles, like and ?

Select all that apply

A
They are always complementary.
B
They are always supplementary.
C
They are always congruent.
D
They are not related.

Check my answer (3)

Which of the following statements is always true about same side interior pairs of angles, like and ?

Select all that apply

A
They are always complementary.
B
They are always supplementary.
C
They are always congruent.
D
They are not related.

Check my answer (3)

Which of the following statements is always true about same side exterior pairs of angles, like and ?

Select all that apply

A
They are always complementary.
B
They are always supplementary.
C
They are always congruent.
D
They are not related.

Check my answer (3)

C-3 Parallel Lines Conjecture

If two parallel lines are cut by a transversal, then corresponding angles are _____, alternate interior angles are _____, and alternate exterior angles are _____.

Select all that apply

A
congruent, congruent, congruent
B
congruent, supplementary, congruent
C
supplementary, supplementary, supplementary
D
supplementary, congruent, supplementary

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Investigation #2

In this investigation, we will create the congruent angles first, then observe the relationship between the lines we create. 1. Change the angle tool to an angle with given size tool. 2. Click B, then D, then change the angle measure to 65

. Change the direction to clockwise before clicking ok. 3. Use the line tool to create line B'D. 4. Change the angle with given size tool to the slope tool. 5. Click lines B'D and AB to measure the slopes. 6. Complete the questions below based on your observations.

Observation

Which of the following statements is true about the slopes of the lines cut by transversal CB?

Select all that apply

A
The slopes are opposite reciprocals, which means the lines are perpendicular.
B
The slopes are opposite reciprocals, which means the lines are parallel.
C
The slopes are equal, which means the lines are perpendicular.
D
The slopes are equal, which means the lines are parallel.

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C-4 Converse of the Parallel Lines Conjecture

If two lines are cut by a transversal to form pairs of congruent corresponding angles, congruent alternate interior angles, or congruent alternate exterior angles, then the lines are _____.

Select all that apply

A
parallel
B
perpendicular
C
intersecting

Check my answer (3)

2.6 Special Angles on Parallel Lines

Investigation #1

Use this figure for Investigation #1

Observation

C-3 Parallel Lines Conjecture

Investigation #2

Observation

C-4 Converse of the Parallel Lines Conjecture

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