In this lesson, students create conjectures about angle relationships and prove them using what they know about rigid transformations. Writing a proof is a multi-step process, and this lesson engages students in several of them. To write a proof, students must generate a conjecture based on observations and calculations. Mathematicians often work collaboratively to brainstorm additional information to develop a proof, demonstrated here in a character scenario. In the next activity students engage in both of these steps. Students begin to label and mark figures to indicate congruence which helps them communicate more precisely.

Students are asked to make viable arguments and critique the reasoning of others when they write convincing explanations for why vertical angles are congruent (MP3). Students are not expected to write formal proofs in this lesson, but they are building their justification skills and working toward that goal.

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.

Today’s community building centers on the teacher sharing their draft commitments as part of the mathematical community. At the end of the lesson, students are invited to suggest additions to the teacher sections of the chart.