Students build on the angle relationships they established in previous lessons to prove the sum of the measures of the angles in a triangle is 180 degrees. In grade 8, students used informal arguments to prove the Triangle Angle Sum Theorem. This lesson revisits that work and takes it further by using more rigorous definitions and careful reasoning. Students will continue developing their skills in writing proofs in subsequent units.
Students work on two proofs. Similar to the previous lesson, one proof uses a 180 degree rotation and the other uses translations. Students make use of structure when they compare various triangles and observe that the same arguments work to prove the Triangle Angle Sum Theorem regardless of what triangle they start with (MP7).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 21.1 Warmup: What Went Wrong? (10 minutes)
 21.2 Activity: Triangle Angle Sum One Way (15 minutes)

21.3 Activity: Triangle Angle Sum Another Way (10 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 21.4 Cooldown: Triangle Angle Sum a Third Way (5 minutes)
Learning goals:
 Prove (in writing) that the sum of the measures of the angles in a triangle is 180 degrees.
Learning goals (student facing):
 Let’s prove the Triangle Angle Sum Theorem.
Learning targets (student facing):
 I can prove the angles in a triangle sum to 180 degrees.
Required materials:
 Geometry toolkits
Standards:
 This lesson builds on the standards: CCSS.8.G.A.5MS.8.G.5CCSS.HSGCO.A.1MS.GCO.1CCSS.HSGCO.A.2MS.GCO.2CCSS.HSGCO.A.4MS.GCO.4CCSS.HSGCO.C.9MS.GCO.9MO.8.GM.A.5cMO.G.CO.A.1MO.G.CO.A.2MO.G.CO.A.4MO.G.CO.C.8
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