Proofs of Known Facts

1. Proofs of Known Facts 8/21/13

2. Objectives • You will be able to write unknown angles proofs involving known facts

3. Warm-up Fill-in the blank. • A ______ of a mathematical statement is a detailed explanation of how that statement follows logically from other statements already accepted as true. • A _______ is a mathematical statement that is proven to be true. • A _______ is a mathematical statement that is given to be true and does not need to be proven.

4. Discussion

5. Lets Recap • You now have available the following facts: • Vertical angles are congruent (VAT) • Alternate interior angles are congruent (AIAT) • Corresponding angles are congruent (Corr. Angles Thm.)

6. Challenge Use any or all of these facts to prove that interior angles on the same side of the transversal are supplementary. Add any necessary labels to the diagram below, then write out a proof – including given facts and a statement of what needs to be proved.

7. Example 1 Use any of these four facts to prove that the three angles of a triangle sum to 180. For this proof, you will need to draw an auxiliary line, parallel to one of the triangle’s sides and passing through the vertex opposite that side. Add any necessary labels and write out your proof.

9. Example 2

10. Converses Each of our parallel lines theorems has a converse theorem. A converse is a statement that reverses the original, or switches the hypothesis with the conclusion.

11. Example 3