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Patty Paper Day 2

Patty Paper Day 2. Tuesday 8/27 Wednesday 8/28 Write this is your Table of Contents. Warm-up. Explain the relationship between vertical angles in complete sentences (e.g. what is the Vertical Angle Conjecture?).

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Patty Paper Day 2

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  1. Patty Paper Day 2 Tuesday 8/27 Wednesday 8/28 Write this is your Table of Contents

  2. Warm-up • Explain the relationship between vertical angles in complete sentences (e.g. what is the Vertical Angle Conjecture?). • Include a description of how you used patty paper to discover the relationship.

  3. Agenda • Warm-up • Class Website • Finish Patty Paper Investigations • Break • Notes on Angle Relationships • Proofs • Assignment

  4. Patty Paper • Step 1: Trace angles 1-4 on your patty paper • Step 2: Using your patty paper, compare the corresponding angles. Write down what you notice. • Step 3: Using your patty paper, compare the alternate interior angles. Write down what you notice. • Step 4: Using your patty paper, compare alternate exterior. Write down what you notice. • Step 5: Determine how Same-Side interior angles are related • Step 6: Complete the following conjecture. • Parallel Lines Conjecture: If two parallel lines are cut by a transversal, then corresponding angles, alternate interior angles, and alternate exterior angles are ___________, and same-side interior angles are ____________.

  5. Break

  6. Recap Euclid’s Axioms • A1: Through any two points, you can draw exactly one line • A2: Given a line L and a point A not on L, there is exactly one line M going through A parallel to L • A3: Corresponding angles are congruent.

  7. Classwork: Now, prove it! • Use Euclid’s Axioms to prove at least two (2) of the following: • PROVE that vertical angles are congruent • Hint: Use supplemental angles • PROVE that alternate interior angles are congruent • Hint: Use Euclid’s A3 • PROVE that alternate exterior angles are congruent • Hint: Use Euclid’s A3 and Vertical Angles • PROVE that same-side interior angles are supplementary • Hint: Use Euclid’s A3 and supplementary angles

  8. Assignment: Parallel Lines Practice • Parallel Problems 1-8 • Subscribe to Class Website

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