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2.3 Homework Answers

10.) Inductive Reasoning12.) Valid

16.) Invalid    18.) Invalid

20.) A; Complementary angles are n...
2.4 Homework Answers

12.) Conditional: If a lunar eclipse occurs, then Earth is
between the Sun and the Moon.          Co...
2.5 Homework Answers

8.) Statements         Reasons
    1. C = 9f + 90     Given
    2. 102 = 9f + 90   Substitution
    ...
Opener:

Have you ever wanted something so bad that you had to fight
for it? (NOT literally!) Maybe it was an allowance ra...
2.6 Proof Strategy:

     Start with the hypothesis of the conditional, given          Hypothesis or 
                    ...
Given: L1 and L2 form a linear pair
     Prove: L1 and L2 are supplementary

                Statements                   ...
Given: L1 and L2 are supplementary
            L2 and L3 are supplementary
     Prove: L1 ≅ L3

                Statements...
Given: LA and LB are right angles
 Prove: LA ≅ LB


          Statements                          Reasons
________________...
Given: L1 and L2 are complementary
       L2 and L3 are complementary
Prove: L1 ≅ L3
          Statements                 ...
Reference Sheet for Proofs: 

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


...
Proof Writing 101:

    1. Start with 2 columns, labeled Statements & Reasons

    2. Number your statements and reasons s...
Partner Practice... Work with your partner on the following (this is your 
homework!)

              Pg. 113 #4‐6, 8, 9, 1...
Exit Slip

Work with you partner to complete and turn
in Pg. 103 # 1- 18 Even. When you are
finished you can begin your ho...
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2.3 Homework Answers

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2.3 Homework Answers

  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

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