Special Angles Formed by Parallel Lines
Geometry in the Trees
Angles Unlimited
A Patty Paper Investigation
Materials Needed:
Ruler
Patty Paper (or tracing paper)
Protractor
1. Use the lines on a sheet of notebook paper or use both edges of your ruler to draw a pair of
parallel lines. Label the lines m and l. Now draw a line that intersects both lines m and l. This is
called a transversal. Label the transversal t. Label the angles 1-8 as shown.
2. Place a piece of patty paper over the set of angles 1, 2, 3, and 4. Trace the two intersecting
lines l and t and the four angles onto the patty paper. Slide the patty paper down to the
intersection of lines t and m and compare angles 1-4 with each of the corresponding angles 5-8.
Based on activities from Key Curriculum Press:
http://wveis.k12.wv.us/Teach21/CSO/Upload/LP2023WS1.doc?tsele1=2&tsele2=117&tsele3i=2023
Special Angles Formed by Parallel Lines
3. What is the relationship between corresponding angles?
4. What is the relationship between alternate interior angles?
5. What is the relationship between alternate exterior angles?
6. Now draw another line that intersects line t but is not parallel to m and l. Label the line n and
the new angles formed 9-12 as shown.
7. Now place your patty paper over the new angles. What do you notice about the corresponding
angles?
8. What do you notice about the alternate interior angles?
9. What do you notice about the alternate exterior angles?
10. Make a conjecture about parallel lines and alternate interior angles, corresponding angles and
alternate exterior angles.
11. Make a conjecture about nonparallel lines and alternate interior angles, alternate exterior
angles and corresponding angles.
Based on activities from Key Curriculum Press:
http://wveis.k12.wv.us/Teach21/CSO/Upload/LP2023WS1.doc?tsele1=2&tsele2=117&tsele3i=2023
Special Angles Formed by Parallel Lines
Geometry in the Trees
Angles Unlimited
A Patty Paper Investigation ANSWER KEY
Materials Needed:
Ruler
Patty Paper (or tracing paper)
Protractor
1. Use the lines on a sheet of notebook paper or use both edges of your ruler to draw a pair of
parallel lines. Label the lines m and l. Now draw a line that intersects both lines m and l. This is
called a transversal. Label the transversal t. Label the angles 1-8 as shown.
2. Place a piece of patty paper over the set of angles 1, 2, 3, and 4. Trace the two intersecting
lines l and t and the four angles onto the patty paper. Slide the patty paper down to the
intersection of lines t and m and compare angles 1-4 with each of the corresponding angles 5-8.
Based on activities from Key Curriculum Press:
http://wveis.k12.wv.us/Teach21/CSO/Upload/LP2023WS1.doc?tsele1=2&tsele2=117&tsele3i=2023
Special Angles Formed by Parallel Lines
3. What is the relationship between corresponding angles? Corresponding angles are congruent
when the lines are parallel.
4. What is the relationship between alternate interior angles? Alternate interior angles are
congruent when the lines are parallel.
5. What is the relationship between alternate exterior angles? Alternate exterior angles are
congruent when the lines are parallel.
6. Now draw another line that intersects line t but is not parallel to m and l. Label the line n and
the new angles formed 9-12 as shown.
7. Now place your patty paper over the new angles. What do you notice about the corresponding
angles? Corresponding angles are not congruent when the lines are not parallel.
8. What do you notice about the alternate interior angles? Alternate interior angles are not
congruent when the lines are not parallel.
9. What do you notice about the alternate exterior angles? Alternate exterior angles are not
congruent when the lines are not parallel.
10. Make a conjecture about parallel lines and alternate interior angles, corresponding angles and
alternate exterior angles. If two parallel lines are cut by a transversal, then alternate interior
angles, corresponding angles and alternate exterior angles are congruent.
11. Make a conjecture about nonparallel lines and alternate interior angles, alternate exterior
angles and corresponding angles. If two non-parallel lines are cut by a transversal, then alternate
interior, corresponding, and alternate exterior angles are not congruent.
Based on activities from Key Curriculum Press:
http://wveis.k12.wv.us/Teach21/CSO/Upload/LP2023WS1.doc?tsele1=2&tsele2=117&tsele3i=2023