In this lesson 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 see three different ways of proving this theorem to allow them to focus on their justification skills without needing to make multiple conjectures.

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.