Download Chapter 2 answers 2016

2.5 Using Algebraic Properties
Name: ________________________
Identify the property that justifies each statement.
1.
Reflexive
9. Addition
17. Substitution
2. Transitive
10. Division
18. Substitution
3. Symmetric
11. Symmetric
19. Multiplication
4. Transitive
12. Multiplication
20. Distributive
5. Subtraction
13. Substitution
21. Substitution
6. Reflexive
14. Addition
22. Multiplication
7. Substitution
15. Transitive
23. Transitive
8. Reflexive
16. Subtraction
Give the reason for each step
24.
8x  34  6
8x  40
x 5
Given
Addition
Division
25.
5  x  3  4  x  2
Given
5x  15  4 x  8
Distributive
x  15  8
x  23
Subtraction
Addition
Use the property to complete the statement.
26. SE
34. mE  mG .
27. mJKL  mRST
35.  x TU  .
28. mJ  mL
36.  m2 .
29.  TU  20 .
37. a  de .
30.  3 m2 .
38. r  5 3c   7 .
31.  100 .
32. is a real number.
33.  AB .
Give the reason for each step
39.
4 x  7  6x  7
2x  7  7
 2x  14
x  7
Given
Subtraction
Addition
Division
40.
1
y9
7
1
x 9 y
7
7x  63  y
y  7x  63
x
Given
Addition
Multiplication
Symmetric
Solve each equation. Give a reason for each step.
41. 7x  11  4 x  19
3x  11  19
3x  30
x  10
4  2x  11  76
43.
Given
Subtraction
Addition
Division
Given
8x  44  76
Distributive
8x  32
x 4
Subtraction
Division
42. 14 x  3  19x  23 Given
5x  3  23
 5x  20
x  4
Subtraction
Subtraction
Division
14  x  1  7  4  x 
14 x  14  28  7x
44. 21x  14  28
21x  42
x  2
Given
Distributive
Addition
Subtraction
Division
Worksheet 2-2 Conditional Statements PAP Answers
Rewrite the conditional statement in if-then form.
1. If a car has leaking antifreeze, then it has a problem.
2. If you don’t have something nice to say, then don’t say anything at all.
3. If a dog is old, then you can’t teach it new tricks.
4. If a blood vessel carries blood toward the heart, then it is a vein.
5. If the time is 6 P.M., then it is time for dinner.
6. If an angle measures more than 90 and less than 180 , then it is an obtuse angle.
Write the converse, inverse, and contrapositive of each statement. (for #9-10 write
the if-then also.)
7. Converse: If you go to the football game, then you like football.
Inverse: If you don’t like football, then you don’t go to the football game.
Contrapositive: If you don’t go to the football game, then you don’t like football.
8. 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.
9. Conditional: If a circle has a radius of r , then it has a circumference of 2 r .
Converse: If the circumference of a circle is 2 r , then a circle has a radius of r .
Inverse: If a circle doesn’t have a radius of r , then it doesn’t have a circumference of 2 r .
Contrapositive: If the circumference of a circle is not 2 r , then a circle doesn’t have a
radius of r .
10. Conditional: If two angles are adjacent, then they share a common side.
Converse: If two angles share a common side, then they are adjacent.
Inverse: If two angles are adjacent, then they share a common side.
Contrapositve: If two angles don’t share a common side, then they are not adjacent.
Write the converse of each true statement. If the converse is also true, combine the
statements to write a true biconditional statement.
11. If an angle measures 30 , then it is acute.
Converse: If an angle is acute, then it measure 30. (F)
12. If two angles are supplementary, then their sum is 180 .
Converse: If 2 angles sum is 180, then 2 angles are supplementary.(T) Two angles are
supplementary if and only if their sum is 180 degrees.
13. If two circles have the same diameter, then they have the same circumference.
Converse: If two circles have the same circumference, then they have the same
diameter.(T) Two circles have the same circumference if and only if they have the same
diameter.
14. If an animal is a panther, then it lives in the forest.
Converse: If an animal lives in the forest, then it is a panther.(F)
In a plane, point F lies between points C and D and EF intersects CD so
That CFE  DFE . Decide whether the given statement is true. Explain
your answer using definitions and properties that you have learned. (draw picture)
15. (False)
16. (True) share a common side and vertex.
17. (False)
18. (True) 2 adjacent angles whose noncommon side form opposite rays.
19. (False)
20. (True) 2 congruent supplementary angles must be right angles.
Decide whether the statement is true or false. If false, provide a counterexample.
21. (True)
22. (False, if could be -6)
(False, 9 is less than 10 and is not prime)
Extra Practice with 2.1 and 2.3
1. Law of Detachment
2. Invalid
3. Law of Detachment
4. Law of Syllogism
5. Invalid
6. Law of Syllogism
7. Deductive, it is logic and order
8. Inductive, based on observations.
9. Inductive, based on observations.
10. Deductive, based on logic and order.
11. Your team wins the baseball game.
12. Callie is also promoted.
13. Kendra won the race.
14. The sum is an integer.
15. 2x<x
16. The quotient is a factor of x.
17. If Moose is hungry when he goes to the pizza shop, then he drinks a pitcher of soda.
18. If you mail the payment by noon, then you won’t be charged a late fee.
19. If Estelle takes her broker’s advice, then she’ll earn 50% on her investment by next year.
20. If a triangle has two angles of 60 , then it is also equilateral.
21. Law of Syllogism.
22. Law of Detachment
23. Neither.