Lesson: Lesson 5: Calculating Missing Angles in Parallel Lines Cut By a Transversal
Lesson Objective
Lesson Plan
Opening
Review Angle Relationships from Lesson 4. Have students silently complete the table for Alternate Interior, Alternate Exterior, Corresponding, and Vertical.
Circulate to check students’ progress and accuracy, then have student volunteers fill in the table.
Have students complete the rest of the page, then go over it.
Example 1: Solve for x in terms of Parallel Lines Cut by Transversals
 Identify the angle relationship: Supplementary
(corresponding, supplementary, alternate interior, or alternate exterior)
This is a great opportunity to review obtuse/acute. Some questions to ask: Which angle is obtuse? Which angle is acute? Since one is acute and one is obtuse can they be congruent? Why or why not? Since they are not congruent, what does that mean? How do you know they add up to 180? How could you prove that using angle relationships?
 That means the angles…add up to 180 degrees
 Set up the equation where angles add up to 180.
 Solve the equation for x
 Check by substitution
 Have students complete You Try 1
Example 2: Find the Measure of Angles in Parallel Lines Cut By A Transversal
 Identify the angle relationship: Alternate Exterior to solve for x.
(corresponding, supplementary, alternate interior, or alternate exterior)
 That means the angles…are equal to each other
 Set up the equation where angles are equal to each other
 Solve the equation for x
 Plug x back into the angle expression to find the angle measure
 Write in on the diagram and explicitly model as “best practice” for students
 Identify the angle relationship: supplementary to solve for x.
(corresponding, supplementary, alternate interior, or alternate exterior)
 That means the angles…add up to 180
 Set up the equation where angles add up to 180
 Subtract to find angle HFE
 Ask students, what’s the difference between this problem and Example 1? (One you solve for X and not plug it back in.)
 Have students complete You Try 2
Common Blunders:
 Students identify the incorrect relationship
 Students mix up congruent and supplementary
 Students mix up alternate exterior and alternate interior
 Students interchange the words complementary and congruent
 Students solve for X and stop
 Students plug in for the angle measure when they should only solve for X
Student Work Analysis
Have students apply their knowledge to identify the student mistake (should be corresponding angles so equations are equal to each other). Circulate, asking guiding questions (as seen above). Discuss the students’ mistakes. Have students solve the problem correctly in the box.
Closing
Have students share out and summarize what they learned today.
Assessment
Have students complete the Exit Ticket
Reflection:
What works: Students learn to set up equations effectively and solve for x, as well as take it to the next level by solving for the missing angle. Also, several diagrams are not drawn to scale which invite an interesting discussion.
What didn't work: Although there are some explicit scaffolds to help students through their thinking, they had a difficult time internalizing the guiding questions. I would add a section where students have to write out/articulate the questions they should ask themselves – almost like a student thinkaloud. The metacognitive piece is crucial as my students were not asking themselves “What makes logical sense? What’s the next piece of information you need and how are you going to find it?”
Lesson Resources
Unit 5 Lesson 5 Calculating Missing Angles Parallel Lines Cut By a Transversal HW.docx 
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Unit 5 Lesson 5 Calculating Missing Angles Parallel Lines Cut By a Transversal.docx 
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