# Lesson: Lesson 5: Calculating Missing Angles in Parallel Lines Cut By a Transversal

4782 Views
13 Favorites

### Lesson Objective

SWBAT Calculate Angle Measures in Parallel Lines Cut By A Transversal Using Algebra

### 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

1. 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?

1. That means the angles…add up to 180 degrees
2. Set up the equation where angles add up to 180.
3. Solve the equation for x
4. Check by substitution
5. Have students complete You Try 1

Example 2: Find the Measure of Angles in Parallel Lines Cut By A Transversal

1. Identify the angle relationship: Alternate Exterior to solve for x.

(corresponding, supplementary, alternate interior, or alternate exterior)

1. That means the angles…are equal to each other
2. Set up the equation where angles are equal to each other
3. Solve the equation for x
4. Plug x back into the angle expression to find the angle measure
5. Write in on the diagram and explicitly model as “best practice” for students

1. Identify the angle relationship: supplementary to solve for x.

(corresponding, supplementary, alternate interior, or alternate exterior)

1. That means the angles…add up to 180
2. Set up the equation where angles add up to 180
3. Subtract to find angle HFE
4. Ask students, what’s the difference between this problem and Example 1? (One you solve for X and not plug it back in.)
5. Have students complete You Try 2

Common Blunders:

1. Students identify the incorrect relationship
2. Students mix up congruent and supplementary
3. Students mix up alternate exterior and alternate interior
4. Students interchange the words complementary and congruent
5. Students solve for X and stop
6. 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 think-aloud. 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 1,149 Unit 5 Lesson 5 Calculating Missing Angles Parallel Lines Cut By a Transversal.docx 1,395