Study Guide and Review Determine whether each conjecture is true or false. If false, give a counterexample. are supplementary angles, then form a linear pair. 11. If ANSWER: False; two nonadjacent supplementary angles 12. If W(–3, 2), X(–3, 7), Y(6, 7), Z(6, 2), then quadrilateral WXYZ is a rectangle. ANSWER: true 13. PARKS Jacinto enjoys hiking with his dog in the forest at his local park. While on vacation in Smoky Mountain National Park in Tennessee, he was disappointed that dogs were not allowed on most hiking trails. Make a conjecture about why his local park and the national park have differing rules with regard to pets. ANSWER: Sample answer: Dogs or other pets may threaten or chase wildlife that might not be present in his local park. Use the following statements to write a compound statement for each conjunction or disjunction. Then find its truth value. Explain. p : A plane contains at least three noncollinear points. q: A square yard is equivalent to three square feet. r: The sum of the measures of two complementary angles is 180. 14. ANSWER: A square yard is not equivalent to three square feet or the sum of the measures of two complementary angles is 180º; true. 15. ANSWER: A plane contains at least three noncollinear points and the sum of the measures of two complementary angles is not 180; true. 16. ANSWER: A plane does not contain at least three noncollinear points or a square yard is equivalent to three square feet; false. 17. PETS The Venn diagram shows the results of a pet store survey to determine the pets customers owned.
a. How many customers had only fish? b. How many had only cats and dogs? c. How many had dogs as well as fish? eSolutions Manual - Powered by Cognero ANSWER:
a. 18 b. 14
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16. ANSWER: Study Guide and Review A plane does not contain at least three noncollinear points or a square yard is equivalent to three square feet; false. 17. PETS The Venn diagram shows the results of a pet store survey to determine the pets customers owned.
a. How many customers had only fish? b. How many had only cats and dogs? c. How many had dogs as well as fish? ANSWER: a. 18 b. 14 c. 22 Determine the truth value of each conditional statement. If true, explain your reasoning. If false, give a counterexample. 18. If you square an integer, then the result is a positive integer. ANSWER: true 19. If a hexagon has eight sides, then all of its angles will be obtuse. ANSWER: true 20. Write the converse, inverse, and contrapositive of the following true conditional. Then, determine whether each related conditional is true or false. If a statement is false, find a counterexample. If two angles are congruent, then they have the same degree measure. ANSWER: Converse: If two angles have the same degree measure, then they are congruent. True. Inverse: If two angles are not congruent, then they do not have the same degree measure. True. Contrapositive: If two angles do not have the same degree measure, then they are not congruent. True. Draw a valid conclusion from the given statements, if possible. Then state whether your conclusion was drawn using the Law of Detachment or the Law of Syllogism. If no valid conclusion can be drawn, write no valid conclusion and explain your reasoning. 21. Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram. The diagonals of quadrilateral PQRS bisect each other. ANSWER: PQRS is a parallelogram; Law of Detachment. 22. Given: If Liana struggles in science class, then she will receive tutoring. If Liana stays after school on Thursday, then she will receive tutoring. ANSWER: Page 2 Invalid; the Law of Syllogism does not apply since the conclusion of the first statement is not the hypothesis of the second statement.
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21. Given: If a quadrilateral has diagonals that bisect each other, then it is a parallelogram. The diagonals of quadrilateral PQRS bisect each other. ANSWER: Study Guide Review PQRS is aand parallelogram; Law of Detachment. 22. Given: If Liana struggles in science class, then she will receive tutoring. If Liana stays after school on Thursday, then she will receive tutoring. ANSWER: Invalid; the Law of Syllogism does not apply since the conclusion of the first statement is not the hypothesis of the second statement. 23. EARTHQUAKES Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain. Given: If an earthquake measures a 7.0 or higher on the Richter scale, then it is considered a major earthquake that could cause serious damage. The 1906 San Francisco earthquake measured 8.0 on the Richter scale. Conclusion: The 1906 San Francisco earthquake was a major earthquake that caused serious damage. ANSWER: Valid; Law of Detachment State the property that justifies each statement. 29. If 7(x – 3) = 35, then 35 = 7(x – 3). ANSWER: Symmetric Property 30. If 2x + 19 = 27, then 2x = 8. ANSWER: Subt. Prop. 31. 5(3x + 1) = 15x + 5 ANSWER: Distr. Prop. 32. 7x – 2 = 7x – 2 ANSWER: Reflex. Prop. 33. If 12 = 2x + 8 and 2x + 8 = 3y, then 12 = 3y. ANSWER: Trans. Prop. 34. Copy and complete the following proof. Given: 6(x – 4) = 42 Prove: x = 3
ANSWER: eSolutions Manual - Powered by Cognero
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Reflex. Prop. 33. If 12 = 2x + 8 and 2x + 8 = 3y, then 12 = 3y. ANSWER: Study Guide and Review Trans. Prop. 34. Copy and complete the following proof. Given: 6(x – 4) = 42 Prove: x = 3
ANSWER:
35. Write a two-column proof to show that if PQ = RS, PQ = 5x + 9, and RS = x – 31, then x = –10. ANSWER: Statements (Reasons) 1. PQ = RS, PQ = 5x + 9,RS = x – 31 (Given) 2. 5x + 9 = x – 31 (Subs. Prop.) 3. 4x + 9 = –31 (Subt. Prop.) 4. 4x = –40 (Subt. Prop.) 5. x = –10 (Div. Prop.) 36. GRADES Jerome received the same quarter grade as Paula. Paula received the same quarter grade as Heath. Which property would show that Jerome and Heath received the same grade? ANSWER: Trans. Prop.
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