## 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.

Big Idea: