1. Lesson 1.6 Paragraph Proofs Objective: Write paragraph proofs

2. Although most proofs we do in this class are two- column, you also need to be familiar with paragraph proofs. Paragraph proofs are useful to know because they help us to think logically through a problem, and put a solution in a form that everyone can understand and follow. We are going to see how to write a paragraph proof, as well as how to show that a conclusion cannot be proved. Why are we doing this?

3. Proof: Since 30’ = ½° we know that 37° 30’ = 37 ½°. Therefore ( ). w 5 or Q.E.D Example #1 x y Given: <x = 37 ½° <y = 37° 30’ Prove: W 5 = which was what was wanted Q.E.D. = Quod Erat Demonstrandum which means “Which was to be Demonstrated”

4. Proof: According to the diagram, <ABC is a straight angle. Therefore, 2x + x = 180 3x = 180 x = 60 Since <DBC = 60° and <E = 60°, the angles are congruent. Q.E.D Example #2 D E Given: Diagram Shown Prove: AB C 60° (2x)° x°x°

5. Not all proofs can be proved. If this happens, we use what’s called a counter-example. We assume that the original statement is true, and then use a specific example to show that it is not possible. Remember, it only takes one false example to disprove a statement! One last thing to keep in mind…

6. Proof: Since <1 is acute, let it be 50°, and since <2 is acute, let it be 30°. Therefore, by counter-example, it cannot be proved that. Q.E.D Example #3 Given: <1 is acute <2 is acute Prove: 21

7. Lesson 1.6 Worksheet Homework