## HSG-CO.C.9

## Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.

48 Lesson(s)

#### Students will draw and measure to discover relationships of angles formed by parallel lines cut by a transversal.

#### Name that transformation! Students will work at identifying transformations performed upon geometric figures.

#### Students will build on prior knowledge about the relationships between angles and parallel lines to write formal proofs.

#### Using conjectures about intersections to justify a claim: students find the right argument to make their case.

#### More basics of Geometry: Drawing diagrams, identifying and naming angles and angle pairs, and solving algebraic problems involving angle pairs. And an answer to that eternal question - why can't we just measure instead of doing constructions?

#### Given a set of definitions, students will try to find counterexamples while applying their understanding of basic geometry vocabulary, particularly types of angles.

#### Students will write precise definitions based on examples and non-examples and test these definitions by looking for counterexamples.

#### Challenge students to prove what they know about parallel lines and angle relationships when the diagram is unique and exact angle measures irrelevant.

#### Students will apply postulates to write two column proofs using vertical angles, complementary angles and supplementary angles.

Big Idea:

#### Students will explore the equality postulates used in geometric proofs.

#### Students are introduced to the two-column proof, and put this knowledge to work on vertical angles and the angle pairs created by parallel lines and transversals.

#### By working several different students, focusing on justification, and revising work after giving and receiving peer feedback, students will justify their reasoning about vertical angles and angles formed by parallel lines.

Big Idea: