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1. 1. 2.3 Homework Answers 10.) Inductive Reasoning12.) Valid 16.) Invalid 18.) Invalid 20.) A; Complementary angles are not necessarily adjacent so they may not form a right angle. 26.) Either Andre is less than 35 years old, or he is not a natural-born citizen. Among the possible answers: Since there are 3 criteria to be eligible and he meets 1, he must not meet 1 of the remaining 2. 1
2. 2. 2.4 Homework Answers 12.) Conditional: If a lunar eclipse occurs, then Earth is between the Sun and the Moon. Converse: If Earth is between the Sun and the Moon, then a lunar eclipse occurs. 16.) False; possible answer: Felipe could be a swimmer 22.)no; possible answer: y = -8 2
3. 3. 2.5 Homework Answers 8.) Statements Reasons 1. C = 9f + 90 Given 2. 102 = 9f + 90 Substitution 3. 12= 9f Subtraction Property of Equality 4. f = 4/3 Division Property of Equality. 10.) Definition of congruent segments; Substitution; Subtraction Property of Equality; Subtraction Property of Equality; Division Property of Equality 12.) Reflexive Property of Congruence 14.) Symmetric Property of Equality 50.) Inductive Reasoning 3
4. 4. Opener: Have you ever wanted something so bad that you had to fight for it? (NOT literally!) Maybe it was an allowance raise, a car, your own room, or a later curfew? What types of justifications did you use or say? Write down what you were arguing/debating for and how you tried to PROVE you were right. 4
5. 5. 2.6 Proof Strategy: Start with the hypothesis of the conditional, given Hypothesis or  Given information, or information in the diagram. *Draw a picture or mark information on a diagram already given. Deductive Reasoning Apply deductive reasoning. *Definitions *Properties *Postulates *Theorems Conclusion Prove that the conclusion of the conditional is true. *Always be thinking about how you can get the conclusion to happen... what makes the conclusion true? 5
6. 6. Given: L1 and L2 form a linear pair Prove: L1 and L2 are supplementary Statements Reasons _______________________________________________________________________________ 6
7. 7. Given: L1 and L2 are supplementary L2 and L3 are supplementary Prove: L1 ≅ L3 Statements Reasons _______________________________________________________________________________ 7
8. 8. Given: LA and LB are right angles Prove: LA ≅ LB Statements Reasons ____________________________________________________________________________ 8
9. 9. Given: L1 and L2 are complementary L2 and L3 are complementary Prove: L1 ≅ L3 Statements Reasons ____________________________________________________________________________ 9
10. 10. Reference Sheet for Proofs:  Get out a clean sheet of paper.  Label one side Definitions and the  other side Theorems. 10
11. 11. Proof Writing 101: 1. Start with 2 columns, labeled Statements & Reasons 2. Number your statements and reasons so that they match *Reason #1 has information about Statement #1 *Reason #3 explains how to move from statement #2 to #3 3. Do NOT make your proofs look like the book's proofs *Properties identified by name *Definitions written as "If..., then..." sentences *Theorems written as "If..., then..." sentences 4. Abbreviate when you can 11
12. 12. Partner Practice... Work with your partner on the following (this is your  homework!) Pg. 113 #4‐6, 8, 9, 17‐23 odd, 28, 30 12
13. 13. Exit Slip Work with you partner to complete and turn in Pg. 103 # 1- 18 Even. When you are finished you can begin your homework. 13