Lesson plan

10. Applying angle relationships with auxiliary lines (A)

teaches Common Core State Standards CCSS.Math.Content.8.G.A.5 http://corestandards.org/Math/Content/8/G/A/5
teaches Common Core State Standards CCSS.Math.Practice.MP3 http://corestandards.org/Math/Practice/MP3
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Lesson objective: Solve problems using angle relationships and auxiliary lines.

This lesson provides an opportunity for students to apply their knowledge and understanding of angle relationships formed from parallel lines and transversals to a real-life situation. Students are asked to create two pool shots, find the resulting angle measures, and provide directions for the player.

Key Concept students will use: 

  • The angle sum for any triangle is 180 degrees, and we can informally prove this using the relationships of angles. 

Skills students will use:

  • angle relationships formed from parallel lines and transversals (alternate interior, alternate exterior, corresponding)
  • angle sum of triangles
  • auxiliary lines

Students engage in Mathematical Practice 3 as they determine angle measures that will work for a pool shot and justify their reasoning with angle relationships.  Students create viable arguments and critique the scenarios of other students to determine reasonable answers.

Key vocabulary: 

  • alternate exterior angles
  • alternate interior angles
  • auxiliary lines
  • corresponding angles


Special materials needed:

  • Pool Table image (optional)