Angle Investigation
Activity
The purpose of this activity is to investigate the relationship between angle measures
when two lines are cut by a transversal. Use the blue endpoints of lines m, n, and t to
move the lines and watch how the angles change. Use the checkboxes to turn each set
of angles on and off.
Exercise 1
Check the box next to the words “Corresponding Angles” to turn two
pairs of corresponding angles on. One pair of corresponding angles is
colored purple. The other pair is colored green.
a) What do you notice about the location of the purple angles? What about the
green angles? In your own words describe what it means for angles to be
corresponding.
b) Describe a situation where the purple angles are congruent. Draw a sketch to
accompany your description.
c) Can you find another way to make the purple angles congruent? What
similarities do you notice between the two arrangements?
d) Is it possible to create a situation where all four angles (two purple and two
green) are congruent? Please explain.
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Exercise 2
Uncheck the box next to “Corresponding Angles” and check the box next
to “Alternate Exterior Angles.” Two pairs of alternate exterior angles will
appear – a purple pair and a green pair.
a) What do you notice about the location of these pairs of angles? In particular,
think about how the placement of these purple angles differs from the
placement of the purple angles that appeared when the “Corresponding Angles”
box was checked. In your own words, describe what it means for angles to be
alternate exterior.
b) Describe a situation where the green angles are congruent. Draw a sketch to
accompany your description.
c) Can you find another way to make the green angles congruent? What
similarities do you notice between the two arrangements?
d) Is it possible to create a situation where all four angles (two purple and two
green) are congruent? Please explain.
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Exercise 3
Uncheck the box next to “Alternate Exterior Angles” and check the box
next to “Alternate Interior Angles.” Two pairs of alternate interior angles
will appear – a purple pair and a green pair.
a) What is different about the location of these angles in comparison to the sets of
angles you have seen so far? What is the same? In your own words, describe
what it means for angles to be alternate interior.
b) Describe a situation where the purple angles are congruent. Draw a sketch to
accompany your description.
c) Can you find another way to make the purple angles congruent? What
similarities do you notice between the two arrangements?
d) Is it possible to create a situation where all four angles (two purple and two
green) are congruent? Please explain.
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Exercise 4
Uncheck the box next to “Alternate Interior Angles” and check the box
next to “Consecutive Interior Angles.” Two pairs of consecutive interior
angles will appear – a purple pair and a green pair.
a) What do you notice about the location of these pairs of angles? In particular,
think about how the placement of these purple angles differs from the
placement of the purple angles that appeared when the “Alternate Interior
Angles” box was checked. In your own words, describe what it means for angles
to be consecutive interior.
b) Describe a situation where the green angles are congruent. Draw a sketch to
accompany your description.
c) Can you find another way to make the green angles congruent? What
similarities do you notice between the two arrangements? How do these
findings differ from your findings in Exercises 1, 2, and 3?
d) Move the lines to recreate the diagrams you drew for Exercise 1, Exercise 2, and
Exercise 3. What do you notice about the measures of the green angles in each
of these situations?
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Conclusion
Make a conjecture about each set of angles – corresponding, alternate
exterior, alternate interior, and consecutive interior. In other words,
come up with a rule for each set of angles that describes the relationship
between their measures when the lines are arranged in a particular way.
You may check and uncheck each set of angles if you need to refer back
to them. Write your conjectures in if-then form.
a) Corresponding Angles
b) Alternate Exterior Angles
c) Alternate Interior Angles
d) Consecutive Interior Angles
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