Geometry Agenda. Week 1.5 Objective Grade. Deductive Reasoning Practice

Transcription

1 Name Period Geometry Agenda Week 1.5 Objective Grade Monday September 19, 2016 Tuesday September 20, 2016 Wednesday September 21, 2016 Thursday September 22, 2016 Friday September 23, 2016 Deductive Reasoning Practice Geometric Proof Practice Geometric Proof Day 2 Practice Review STUDY Test Relax First Things First Average *** Reminder: Your test is this FRIDAY. All Unit 2 homework and makeup work is due by the day of the test. NO LATE WORK WILL BE ACCEPTED AFTER THE DAY OF THE TEST.

2 Monday Tuesday Wednesday Thursday Friday No Warm Up

3 Monday Tuesday Wednesday Thursday Friday No Warm Up

4 Geometry: Unit 3 Deductive Reasoning Practice Deductive Reasoning Pages Name: Date: Period: Use the statements in the box below. If Winnie reads the book by Friday, then she will write the report on Saturday. If Winnie writes the report on Saturday, then she will turn it in on Monday. 1. Assume that Winnies reads the book by Friday. What conclusion can you make? Why? 2. Suppose that Winnie does not turn the report in on Monday. What conclusion can you make? Assume the following are true: * If David does not buy popcorn, then he did not shop. * If Ashley buys pizza, then she will have some left over. * If the store is open, then Ashley and David will shop. * If Ashley shops, then she will buy pizza. * The store is open. 3. Did Ashley buy popcorn? 4. Did Ashley have pizza left over? 5. Did David eat part of Ashley s pizza? 6. Did David buy popcorn? Order the statements in the two problems below. Then state the conclusion. 7. Given: 4 60 o m a. If m o, then m 6 60 o. b. m 4 60 o. c. If m o, then m o. d. If m 6 60 o, then m o. e. If m 4 60 o, then m o. Conclusion:

5 Geometry: Unit 3 Deductive Reasoning Determine if each example is using deductive or inductive reasoning. 8. If it is Friday, then Kendra s family has pizza for dinner. Today is Friday, therefore, Kendra s family will have pizza for dinner. 9. For the past three Wednesdays the cafeteria has served macaroni and cheese for lunch. Julie concludes that the cafeteria will serve macaroni and cheese for lunch this Wednesday hooray. 10. If you live in Texas and are 16, then you must take driver s education to get your license. Marcus lives in Texas, is 16 years old, and has his driver s license. Therefore, Marcus took driver s education. INDUCTIVE INDUCTIVE INDUCTIVE DEDUCTIVE DEDUCTIVE DEDUCTIVE 11. The Berkner Rams scored over 75 points for their first ten basketball games. The newspaper predicts that they will score more than 75 points tonight. Which form of reasoning is this conclusion based on? (A) Deductive reasoning, because the conclusion is based on logic. (B) Deductive reasoning, because the conclusion is based on a pattern. (C) Inductive reasoning, because the conclusion is based on logic. (D) Inductive reasoning, because the conclusion is based on a pattern. When Alice meets the Pigeon in Wonderland, the Pigeon thinks she is a serpent. The Pigeon reasons that serpents eat eggs, and Alice confirms that she has eaten eggs. 12. Write Serpents eat eggs as a conditional statement. 13. Is the Pigeon s conclusion that Alice is a serpent valid? Justify your reasoning. 14. If Cassie goes to the skate park, Hanna and Amy will go. If Hanna or Amy goes to the skate park, then Mark will go. If Marc goes to the skate park, then Dallas will go. If only two of the five people went to the skate park, who were they? (A) Hanna and Amy (B) Cassie and Dallas (C) Dallas and Marc (D) Amy and Marc REVIEW: 15. Find the next 3 numbers in this sequence: 1, 5, 25, 125,,,.

6 Geometry: Unit 2 Geometric Proof Practice Geometric Proof Pages 66-68, Name Date Period 1. Given: Prove: Given: NA AM M is the midpoint of AB Prove: NA MB 1. NA AM M is midpt of AB AM MB NA MB 4. A N M B 2. Given: H is the midpoint of GI G JH HI Prove: GH HJ H 5. Given: B is between A & C AB = 9 BC = 7 Prove: 16 = AC A B C H is the midpoint of GI JH HI GH J HI GH HJ I 1. B is between A & C AB = BC = AB + BC = AC = AC = AC Given: V is the midpoint of SW W is the midpoint of VT Prove: SV WT V is the midpoint of SW W is the midpoint of VT SV VW VW WT S T W 6. Given: m 1 m o V Prove: SV WT 1. m 1 m o Def. of supplementary angles 3. 3 & 4 form a 3. Linear pair 4. 3 and 4 are 4. supplementary

7 Geometry: Unit 3 Geometric Proof Day 2 Practice Geometric Proof Day 2 Pages 66-68, Name Date Period 1. A is a statement you can prove. (postulate or theorem) 2. Vertical Angles Theorem - 3. If A and B are vertical angles, then 4. Fill in the blanks for the proof of the Vertical Angles Theorem. Given: 1 and 3 are vertical angles Prove: Fill in the blanks to complete the following proofs. 5. Given: 2 3 Prove: 1 and 3 are supplementary Given 2. m 2 m and 2 form a linear pair Linear Pair Theorem 5. m 1 m Def. of Supplementary Angles 6. m 1 m Def. of Supplementary Angles 6. Given: 1 4 Prove:

8 Geometry: Unit 3 Geometric Proof Day 2 7. Given: BX bisects ABC m ABX 45 Prove: ABC is a right angle 1. BX bisects ABC m ABX m XBC m ABX m XBC m ABX m XBC m ABC = m ABC = m ABC ABC is a right angle 9. A B X C 8. Given: RV bisects SRT 3 1 Prove: S 3 R 1 2 V T 9. Given: AH bisects Prove: m GAH IAG m HAI A G H I State whether each statement is sometimes, always, or never true. 10. An angle and its complement are congruent. 11. A pair of right angles forms a linear pair. 12. An angle and its complement form a right angle. 13. A linear pair of angles is complementary. 14. Find m Find the value of x and then the measures of all 4 angles.

9 Geometry Name Review - Geometric Reasoning Date Period For #1 4, identify the hypothesis and conclusion of the each given statement. 1. Underline the hypothesis: If two rays are opposite rays, then they form a line. 2. Circle the conclusion: If two rays are opposite rays, then they form a line. 3. Underline the hypothesis: Stacey will make an A if she does all of her homework. 4. Circle the conclusion: Stacey will make an A if she does all of her homework. For #5 6, write the inverse, converse, and contrapositive for each statement. Then determine if each statement is true or false. 5. If two rays are opposite rays, then they form a line. Converse: True or False Inverse: True or False Contrapostive: True or False 6. Stacey will make an A if she does all of her homework. Converse: True or False Inverse: True or False Contrapostive: True or False For #7, determine the correct biconditional statement. 7. Which of the following is the biconditional for the statement below If two rays are opposite rays, then they form a line. A. If and only if two rays are opposite rays, then they form a line. B. If two rays are opposite rays, then they form a line. C. Two rays are opposite rays if and only if they form a line. D. If two rays form a line, then they are opposite rays. For #8, determine which statement below is true! 8. Which of the following is the statements is true for the conditional statement below If two lines are parallel, then they have the same slope. A. Converse: If two lines are not parallel, then they have the same slope. B. Inverse: If two lines are not parallel, then they do not have the same slope. C. Contrapositive: If two lines have the same slope, then they are parallel. D. Biconditional: Parallel lines have the same slope if and only if.

10 For #9-10, what can you conclude from the following using the law of syllogism? 9. If I am hungry, then I eat ice cream. If I eat ice cream, then I need a spoon. Conclusion: 10. If two angles are a linear pair, then they add to 180 o. Two angles are supplementary, if they add to 180 o. Conclusion: For #11 14, determine whether each of the problem below uses Inductive or Deductive reasoning. 11. All jeans I own are blue. Inductive Deductive All jeans must be blue. 12. The sum of A and B is Inductive Deductive Complementary angles sum to 90 o. A and B are complementary. 13. All referees I have seen are men. Inductive Deductive Only men can be referees. 14. A triangle with two equal sides is isosceles. Inductive Deductive A triangle with three equal sides is equilateral. If a triangle does not have any equal sides, then it is not isosceles or equilateral. For #15 16, determine the next two items for each pattern , 12, 36, 108,, 16. 5x 6, 10x 10, 15x 14, 20x 18,, For #17 20, state the property being used. 17. If DEF GHI,thenGHI DEF 18. If m A 3 90 o, then m A 30 o 19. COD COD 20. PQ + 4 = RS + 4

11 For #21 23, complete the following algebraic proofs x ( x 2) 4x 3( x 2) Given 22. Use the diagram below to write an algebraic proof. 6x + 5) o (5x - 12) o

12 For #22 25, complete the following geometric proofs. 23. Given: NA AM N M is the midpoint of AB Prove: NA MB A 1. NA AM M is midpoint of AB AM MB NA MB 4. M B 24. Given: 2 3 Prove: 1 and 3 are supplementary Given 2. m 2 m and 2 form a linear pair Linear Pair Theorem 5. m 1 m m 1 m Def. of Supplementary Angles 25. Given: RV bisects SRT 3 1 Prove: RV bisects SRT S 3 R 1 2 V T Which of the following would be the correct for reason #4? A. Definition of Angle Bisector B. Transitive Property of Congruence C. Substitution Property of Congruence D. Segment addition Postulate