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Properties of Parallel Lines 2
In this investigation, you will discover relationships among the angles formed when parallel lines
are cut by a transversal.
Sketch and Investigate
1. In the space below, draw a line and label it AB.
2. Using both sides of a ruler, draw a line parallel to line AB and label a point on this new line C.
3. Draw line CA.
4. Label points D, E, F, G and H as shown below.
Based on activities from Key Curriculum Press
5. Measure the eight angles in your figure and write their measurements below.
Angle DCF _____
Angle FCE _____
Angle DCA _____
Angle ECA _____
Angle GAC _____
Angle CAB _____
Angle GAH _____
Angle HAB _____
6.
When two parallel lines are cut by a transversal, special angle pairs are formed. These
special angle pairs have specific names and properties. The chart below shows one
example of each type of angle pair. Fill in the chart with a second angle pair of each type,
then state what relationship, if any, you observe between the angles in a pair type
.
Angle Type
Corresponding
Alternate interior
Alternate exterior
Same-side interior
angles
Same-side exterior
7.
Pair 1
Angle FCE and Angle
CAB
Angle ECA and Angle
CAG
Angle FCE and Angle
HAG
Angle ECA and Angle
BAC
Angle FCD and Angle
HAG
Pair 2
Relationship
One of the angle types has more four pair. Name that angle type in the chart below, and
name the third and fourth pairs of angles of that type.
Based on activities from Key Curriculum Press
Angle Type
Pair 3
Pair 4
Relationship
8. We will now investigate the converses of your conjectures. In the space below, draw two
lines that are not parallel. Draw a transversal.
9. Add points as needed in order to measure all eight angles formed by the three lines.
Record their measurements below.
10. What do you notice about the corresponding, alternate interior and alternate exterior
angles when the lines are not parallel?
11. What do you notice about the same side interior angles when the lines are not parallel?
Based on activities from Key Curriculum Press
12. Complete: If two lines are cut by a transversal so that corresponding angles, alternate
interior angles, and alternate exterior angles are congruent, and same side interior angles
are supplementary, then...
Geometry in the Trees
Angles Unlimited 2
Properties of Parallel Lines (suggested answers)
1.
Based on activities from Key Curriculum Press
5. Measure the eight angles in your figure and write their measurements below. (Answers will
vary.)
6.
Angle Type
Corresponding
Alternate interior
Alternate exterior
Same-side interior
angles
Same-side exterior
7.
Angle Type
Corresponding
Pair 1
Angle FCE and Angle
CAB
Angle ECA and Angle
CAG
Angle FCE and Angle
HAG
Angle ECA and Angle
BAC
Angle FCD and Angle
HAG
Pair 2
Angle FCD and Angle
CAG
Angle DCA and angle
CAB
Angle FCD and angle
BAH
Angle DCA and Angle
CAG
Angle FCE and Angle
BAH
Relationship
Congruent
Pair 3
Pair 4
Relationship
Angle ECA and angle
BAH
Angle DCA and angle
GAH
Congruent
Based on activities from Key Curriculum Press
Congruent
Congruent
Supplementary
Supplementary
8.
9. Add points as needed. Measure all eight angles formed by the three lines and record their
measurements below. (Answers will vary)
10. What do you notice about the corresponding, alternate interior, and alternate exterior
angles when the lines are not parallel? (They are not congruent)
11. What do you notice about the same side interior angles when the lines are not parallel?
(They are not supplementary.)
12. The lines are parallel
Based on activities from Key Curriculum Press
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