Answer Key Lesson 2.1 Practice Level B 1.
2.
3.
4.
5. add 111 to each term; 557
6. add consecutive integers to each term, starting with 2; 24
7. add 2 to the numerator and 1 to the 9 denominator; } 7
8. subtract 1 from the numerator and 1 from the 3 denominator; }4
9. subtract 3 from each term; 29
10. square numbers; 25
11. double the number and add 1; 47
12. prime numbers; 13
2 13. 16 14. 20 15. Sample answer: } 5 0.5 16. Sample answer: 5 2 7 5 22 4 22 22 1 1
Î14
}
1 1 2 2
1 4
17. Sample answer: } 5 2 18. Sample answer: } 5 } , } > }
1 19. y 5 x 3 20. y 5 2x 2 7 21. y 5 2x 1 5 22. y 5 } x 23. 512 billion bacteria 24. 15 days
Answer Key Lesson 2.2 Practice Level B 1. If it is 6 p.m., then it is time for dinner. 2. If the carton is full, then there are 12 eggs. 3. If an angle is obtuse, then it measures more than 908 and less than 1808. 4. If there is gas in the tank, then the car will run. 5. converse: If you go to the hockey game, then you like hockey; inverse: If you do not like hockey, then
you do not go to the hockey game; contrapositive: If you do not go to the hockey game, then you do not like hockey. 6. converse: If 3x is odd, then x is odd; inverse: If x is not odd, then 3x is not odd; contrapositive: If 3x is not odd, then x is not odd. 7. true 8. false; x 5 66 9. true 10. true 11. If an angle is acute, then it measures 308. 12. converse: If the sum of two angles is 1808, then they are supplementary; biconditional: Two angles are supplementary if and only if their sum is 1808. 13. converse: If two circles have the same circumference, then they have the same diameter; biconditional: Two circles have the same circumference if and only if they have the same diameter. 14. If an animal lives in the forest, then it is a panther. 15. conditional statement: If two lines are perpendicular, then they intersect to form right angles; converse: If two lines intersect to form right angles, then the two lines are perpendicular. 16. conditional statement: If a point is a midpoint of a segment, then it divides the segment into two congruent segments; converse: If a point divides a segment into two congruent segments, then the point is the midpoint of the segment. 17. yes 18. yes 19. No; the angles could be in a triangle. 20. A saxophone that has a frequency of 69 cycles per second to 415 cycles per second is called an E-flat baritone saxophone. 21. A saxophone that has a frequency of 103 cycles per second to 622 cycles per second is called a B-flat tenor saxophone. 22. A saxophone that has a frequency of 138 cycles per second to 830 cycles per second is called an E-flat alto saxophone. 23. The saxophone is an E-flat baritone saxophone. 24. nothing; It could be any of the three saxophones.
Answer Key Lesson 2.3 Practice Level B 1. Law of Detachment 2. invalid 3. Law of Detachment 4. Law of Syllogism 5. invalid 6. Law of Syllogism 7. deductive reasoning; Deductive reasoning is based on logic and order. If Walt is
taller than Peter and Peter is taller than Natalie, then Walt is taller than Natalie. 8. inductive reasoning; Inductive reasoning depends on previous examples and patterns to form a conjecture. If Brand Y costs more than Brand X and Brand X costs more than any other brand, then Brand Y costs more than all other brands. 9. inductive reasoning; Inductive reasoning depends on previous examples and patterns to form a conjecture. Dana came to her conclusion based on previous examples. 10. deductive reasoning; Deductive reasoning is based on logic and order. If Anthony is a 16–18 year old with a license in Nevada, then Anthony must have taken the required driver education. 11. not valid; It does not say that Jeff is not allowed to play video games on Saturday afternoon. It says that he does not play video games on Saturday afternoon. 12. not valid; Katie knows that all sophomores take driver education. It does not say that only sophomores take driver education. You do not know if Brandon is a sophomore. 13. false; The mall is open. Therefore Jodi and Dan went shopping, and therefore Dan bought a pretzel. You cannot conclude that Dan also bought a pizza. 14. true; The mall is open, therefore Jodi and Dan went shopping. 15. true; The mall is open. Therefore Jodi and Dan went shopping, and therefore Jodi bought a pizza. 16. false; The mall is open. Therefore Jodi and Dan went shopping, and therefore Dan bought a pretzel and Jodi bought a pizza. You cannot conclude whether or not Jodi had some of Dan’s pretzel. 17. D, B, A, E, C; The robot extinguishes the fire.
Answer Key Lesson 2.4 Practice Level B 1.
2.
3.
4. Postulate 8: Through any three noncollinear points there exists exactly one plane. 5. Postulate 5: Through any two points there exists exactly one line. 6. Postulate 11: If two planes intersect, then their intersection is a line. 7. Postulate 10: If two points lie in a plane, then the line containing them lies in the plane. 8. No. Through any two points there exists exactly one line. 9. Yes. Points A and B could lie on the line intersecting two planes. 10. Yes. Take point A and any two points on line k and you can form a plane through those three points that
contains all of line k. 11. Yes. The plane that runs from the front of the room to the back of the room through points A and B contains both points and a point on the front wall. 12. true 13. false 14. false 15. false 16. true 17. true 18. false 19. false 20. a.
b. building B c. right d. 2 e. Yes, because ∠ DBE is acute and Building E is due west of Building C.
Answer Key Lesson 2.5 Practice Level B 1. a. Distributive Property b. Addition Property of Equality c. Subtraction Property of Equality 2. a. Addition Property of Equality b. Addition Property of Equality c. Division Property of Equality 3. a. Segment Addition Postulate b.
Substitution Property of Equality c. Distributive Property 4. a. Reflexive Property of Equality b. Addition Property of Equality c. Angle Addition Postulate d. Angle Addition Postulate e. Substitution Property of Equality 5. a. Definition of perpendicular segments and definition of right angle b. Definition of perpendicular segments and definition of right angle c. Substitution or Transitive Property of Equality 6. m∠ B 7. GH, CD 5 RS 8. 17 1 9. RL 5 BC 10. 3(45) 11. } 3 12. C(23, 6), E(5, 0); AB is 5 units long. Because AB 5 CD, then CD is 5 units long. So the
coordinates of C are (23, 6). Because CD 5 OE, then OE is 5 units long. So the coordinates of E are (5, 0). 13.
D 5 0.06t 1 0.11(45 2 t) D 5 0.06t 1 4.95 2 0.11t D 5 0.06t 2 0.11t 1 4.95 D 5 20.05t 1 4.95 0.05t 1 D 5 4.95 0.05t 5 2D 1 4.95 t 5 220D 1 99 14.
Given Distributive Property Group like terms. Simplify. Addition Property of Equality Subtraction Property of Equality Division Property of Equality
D
2.7
3
3.7
4.3
4.5
t
45
39
25
13
9
15.
16. m∠ 1 5 808, m∠ 2 5 808, m∠ 3 5 1208, m∠ 4 5 808, 17. Candidate 1: 22.2%,
Candidate 2: 22.2%, Candidate 3: 33.3%, Candidate 4: 22.2% 18. Candidate 1: 70, Candidate 2: 70, Candidate 3: 105, Candidate 4: 70
Answer Key
Answer Key Lesson 2.6 Practice Level B 1. 1. Given 2. Given 3. Substitution Property
} } of Equality 4. HI > IJ 5. Given 6. Transitive Property of Congruence 2. 1. Given 2. Given 3. Definition of complementary angles 4. Transitive Property of Equality 5. Subtraction Property of Equality 6. Definition of congruent angles 3. 1. Given 2. Reflexive Property of Equality 3. Addition Property of Equality 4. Segment Addition Postulate 5. Segment Addition Postulate 6. Substitution Property of Equality 4. 1. Given 2. Transitive Property of Angle Congruence 3. m∠ 2 5 m∠ 4 4. Substitution Property of Equality 5. x 5 6; Because the angles are congruent, the measures of the angles are congruent by the definition of congruent angles. Set the measure of the angles equal to } } each other to find x. 6. x 5 3; By the transitive property, FG > JH. Set the lengths of the segments equal to each other to find x. 7. x 5 5; By the transitive property, ∠ ABD > ∠ EBC. Because the angles are congruent, the measures of the angles are congruent by the definition of congruent angles. Set the measures of the angles equal to each other to find x. 8. x 5 4; Because the segments are congruent, the lengths of the segments are congruent by the definition of congruent segments. Set the lengths of the segments equal to each other to find x. } } } } 9. UV > ZY, UW > ZX (Given) UV 5 ZY, UW 5 ZX (Def. of >) VW 5 UW 2 UV (Segment Addition Postulate) YX 5 ZX 2 ZY (Segment Addition Postulate) YX 5 UW 2 UV (Substitution Property of Equality) VW 5 YX (Transitive Property of Segment Congruence) } } VW > YX (Def. of >)
Answer Key
Answer Key Lesson 2.7 Practice Level B 1. false 2. true 3. false 4. true 5.
6.
7.
8.
9.
10.
11. x 5 5, y 5 26; 748, 1068, 748, 1068 12. x 5 10, y 5 40; 508, 1308, 508, 1308 13. x 5 7, y 5 9; 368, 1448, 368, 1448 14. x 5 9, y 5 9; 638, 1178, 638, 1178 15. 1. Given 2. Vertical angles are congruent.
3. Transitive Property of Congruence 4. Vertical angles are congruent. 5. Transitive Property of Congruence 16. 1. Given 2. Definition of complementary angles 3. Given 4. Definition of congruent angles 5. Substitution Property of Equality 6. Substitution Property of Equality 7. Definition of complementary angles 17. 5 18. < 19. > 20. 5
Answer Key
