Setting Up Proofs Objectives:  To set up proofs from verbal statements  To prove theorems

Steps to writing a proof for a given theorem: Step 1: Draw and label a diagram. Step 2: Restate the theorem in terms of the labeled diagram. Step 3: Restate what is given, and what is to be proved. The restatement should include the specific rays, segments, angles and other geometric parts from your diagram.

Alert! Sometimes a theorem is written as a simple declarative sentence. The subject of the sentence is the given, and the verb (and remainder of the sentence) is the prove. We will be converting these sentences to if-then form, however.

Example 1 Draw and label a diagram. Restate the theorem in terms of the diagram. State what is given and what is to be proved. Supplementary Angles 1 2 < 1 supp. < 2 <1 ≡ < 2

Example 1 If two congruent angles are supplementary, then they are right angles. Given: Prove: Supplementary Angles 1 2 < 1 supp. < 2; < 1 ≡ < 2

Example 2 Labeled Diagram: If two angles are each congruent to a third angle, then they are congruent to each other. Given: Prove: Draw and label a diagram. Restate the theorem in terms of the diagram. State what is given and what is to be proved.

Final for Understanding Summarize in your own words the steps for setting up a proof from a given statement. Set up a proof based upon the following statement: Complements of vertical angles are congruent. Homework: Setting Up Proofs Worksheet, plus text _____________________