Lunch Lines Task MGSE9-12.G.CO.9
Corresponding Angle Postulate: If two parallel lines are cut by a transversal, then corresponding
angles are congruent.
1. Using this postulate, name the congruent angles.
2. How do we know that ∠3 ≅∠6?
Alternate Interior Angle Theorem: If two parallel lines are cut by a transversal, then alternate
interior angles are congruent.
Alternate exterior angles:
3. Prove this theorem using the figure above.
4. How do we know that ∠3 𝑎𝑛𝑑∠5 are supplementary?
5. Define supplementary.
Same-Side Interior Angle Theorem: If two parallel lines are cut by a transversal, then
same-side interior angles are supplementary.
Same-side exterior angles:
Prove this theorem using the figure above.
Paul, Jane, Justin, and Opal were finished with lunch and began playing with drink straws.
Each one was making a line design using either 3 or 4 straws.
They had just come from math class where they had been studying special angles.
Paul pulled his pencil out of his book bag and labeled some of the angles and lines. He then
challenged himself and the others to find all the labeled angle measurements in Paul and
Justin’s straw designs and to determine whether the lines that appear to be parallel really are
parallel.
Paul’s straw design
A
2C
C
x
y
B
40


z

 2 x  10 
 3x  30 
 5x  20 
Justin’s straw design
Find all of the labeled angle
measurements.
Determine whether the lines
that appear to be parallel really
are parallel.
Explain the reasoning for your
results.
Paul then challenged himself and the others to find all the labeled angle measurements in
Jane and Opal’s straw designs knowing that the lines created by the straws in their designs
were parallel.
Jane’s straw design
y
135
z
x
70


140
x
70
Opal’s straw design
Recall linear pair; define: auxiliary line
Find all of the labeled angle
measurements (knowing that
the lines created by the straws
are parallel).
Explain the reasoning for
your results