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Geometry
Parallel Lines Cut by a Transversal Investigation
Day _____ CW/HW
Name
Date
Block
1. a) In figure A, take a sheet of patty paper and place it over <1 . Using a ruler, make a precise
copy of <1. Slide (translate) the copy of <1 to <5 and compare the sizes of the two angles.
What do you observe?
b) Repeat this process for <1 and <5 in figure B. What do you observe?
c) In figure A, trace a copy of <3 and try to fit it over <6. What do you observe?
d) Repeat this process for <3 and <6 in figure B. What do you observe?
e) Both figures show two lines that are cut by a transversal. Under what condition will certain
pairs of angles be equal?
2. Use what you know about straight angles to calculate the measures of the missing angles:
Write the measure of each angle next to the letter that represents it. (figure not drawn to
scale)
a
107°
c
l
d
e
f
g
m
73°
3. Based on the picture from #2, which of the following angle pairs are congruent? (Circle all
that apply)
Alternate Interior
Same-Side Interior
Corresponding
Alternate Exterior
4. What must be true about lines l and m in order for the angle pairs above to be congruent?
5. Which pair of angles from the picture in #2 was not congruent? What special relationship do
they have? Explain how you know.
6. Complete the following sentences:
a) If 2 parallel lines are cut by a transversal, then alternate interior angles are _____________.
b) If 2 parallel lines are cut by a transversal, then same-side interior angles are ____________.
c) If 2 parallel lines are cut by a transversal, then alternate exterior angles are ____________.
d) If 2 parallel lines are cut by a transversal, then corresponding angles are _______________.
7. Classify each of the following pairs of angles as corresponding, alternate interior, alternate
exterior, same-side interior, supplementary, vertical, or none of these.
a)
b)
c)
d)
e)
f)
g)
h)
i)
a
b
Use what you know about straight angles to calculate the measures of the missing angles: