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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.

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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

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2.5 Homework Answers

8.) Statements Reasons1. C = 9f + 90 Given2. 102 = 9f + 90 Substitution3. 12= 9f Subtraction Property of Equality4. 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

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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.

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2.6 Proof Strategy:

Start with the hypothesis of the conditional, giveninformation, or information in the diagram.

*Draw a picture or mark informationon a diagram already given.

Apply deductive reasoning.

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?

Hypothesis or Given

Deductive Reasoning*Definitions *Properties*Postulates *Theorems

Conclusion

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Given: L1 and L2 form a linear pairProve: L1 and L2 are supplementary

Statements Reasons_______________________________________________________________________________

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Given: L1 and L2 are supplementary L2 and L3 are supplementary

Prove: L1 ≅ L3

Statements Reasons_______________________________________________________________________________

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Given: LA and LB are right anglesProve: LA ≅ LB

Statements Reasons____________________________________________________________________________

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Given: L1 and L2 are complementary L2 and L3 are complementary

Prove: L1 ≅ L3

Statements Reasons____________________________________________________________________________

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Reference Sheet for Proofs:

Get out a clean sheet of paper. Label one side Definitions and the other side Theorems.

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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

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Partner Practice... Work with your partner on the following (this is your homework!)

Pg. 113 #4‐6, 8, 9, 17‐23 odd, 28, 30

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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.