Authentic Lessons for 21st Century Learning

What's Your Angle?

Parallel Lines Cut by a Transversal

K20 Center, Brooke Bean | Published: May 31st, 2022 by K20 Center

  • Grade Level Grade Level 9th, 10th
  • Subject Subject Mathematics
  • Course Course Geometry
  • Time Frame Time Frame 4-5 class period(s)
  • Duration More 200 minutes


Students will explore specific angle pair relationships that are created between a set of parallel lines and a transversal. After an understanding of the angle pairs is developed, students will then create a city map that demonstrates their ability to apply these angle pairs.

Essential Question(s)

In what ways can data be communicated clearly to all audiences?



Engage students with a slide showing how parallels and transversals appear in real life.


Allow students to explore angle pair relationships through measuring different angles that are created by a transversal and finding the angle pairs similarities/characteristics.


Show a video to attach the special angle pair relationships to a specific vocabulary word.


Allow students to create a city or neighborhood that demonstrates these special angle pair relationships in real life.



  • Writing utensil

  • Protractors

  • Rulers (straight edge)

  • Poster board or sticky easel pad paper (one for each group of four)

  • Markers, colored pencils, crayons, etc.

  • Timers


Have the "Real World Parallels and Transversals" slide pulled up on the screen as the students walk in. As a Bell Ringer, direct students to look at the pictures and write down what they see. Once the bell rings or class starts, ask students to share out what they’ve written. Listen for key words like "parallel lines" and "transversals" or at least phrases that function as the definitions of those words.


Have students partner up (you can put them in pairs or let them decide). Pass out the worksheet titled "What's Your Angle" Students will draw a transversal using a ruler. Once they have drawn their lines, they will use their protractors to measure each angle (all 8) to the nearest degree. Once they have measured all 8 angles, have them answer the questions. This worksheet is designed for students to notice different angle pair relationships (alternate interior, alternate exterior, corresponding, consecutive interior, vertical, linear pair).


After each pair has had a chance to answer all of the questions, use Think-Pair-Share and have two pairs join to create groups of 4. Once students are in their group of 4, ask them to answer the question: "How would you describe the relationship between . . . " Select two angles to compare for angles 5-8 and have them describe the relationship between those angles using ONLY 2 WORDS for each angle pair. Have them write those two words on their worksheet next to the corresponding number. After each group has their two words, come together as a class and have each group share what they came up with. See if, as a class, you can all agree on the names of these special angle pair relationships. Follow the discussion with the Parallel Lines and Transversals video.


In this portion, students will choose a group of 4 and create a city, neighborhood, zoo, etc., with roads and walkways as their parallels and transversals. Any building or enclosure would be used to describe an angle pair relationship. Print off 1 rubric for each group, and project the "City Project Example" on your board as an example.


Students will be performing Gallery Walk to display their work and also critique others'. Have the students set their projects up around the room and number each project. Alongside each project, have the students set out a copy of the "Questions - Comments" handout (located under Attachments). The students will each need a copy of the "City Project Critique" handout (also located under Attachments). Have students travel around the room with their group, visiting other groups' projects. At each project, have a member from each group leave a question and a comment. After all groups have had a chance to see every project, they can return to their own projects and read the feedback.