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HW #11—Review for Test #2
Define each of the following; give an example if possible.
1. Reflexive
2. Symmetric
3. Transitive
4. Angle Addition Postulate
5. Segment Addition Postulate
6. definition of angle bisector
7. definition of midpoint
8. definition of complementary
9. definition of supplementary
10. definition of an acute angle
11. definition of a right angle
12. deductive reasoning
13. inductive reasoning
14. conditional
15. hypothesis
16. conclusion
17. converse
18. inverse
19. contrapositive
20. counterexample
21. biconditional
22. Addition Property of Equality
23. Subtraction Property of Equality
24. Multiplication Property of Equality
25. Division Property of Equality
26. Commutative Property of Addition
27. Commutative Property of Multiplication
28. Associative Property of Addition
29. Associative Property of Multiplication
30. Distributive Property
31. Substitution
32. Law of Detachment
33. Law of Syllogism
Name:____________________________________
Period:______
Complete each proof with the appropriate reasons:
35. Geometric Proof:
D
34. Algebraic Proof:
______________________________________________
1. 3 (x – 4) + 9 = 6 (x – 2) 1. ___________________
2.
3x – 12 + 9 = 6 x – 12 2. ___________________
3.
3 x – 3 = 6 x – 12 3. ___________________
4.
– 3 = 3 x – 12
O
G
Given: O is the midpoint of DG
Prove: DO = ½ DG
________________________________________
1. O is the midpt of DG
2. DO
1.________________
OG
2.________________
3. DO = OG
3.________________
4. ___________________
4. DO + OG = DG
4.________________
5.
9 = 3x
5. ___________________
5. DO + DO = DG
5.________________
6.
3 = x
6. ___________________
6. 2 DO = DG
6.________________
7.
x=3
7. ___________________
7. DO = ½DG
7.________________
Write the converse, inverse, and contrapositive of each conditional statement and circle if it is true or false.
If false, give a counterexample.
36. If two angles are complementary, then their sum is 90°.
Converse: _________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Inverse: ____________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Contrapositive:_______________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
37. If two angles are vertical, then they are congruent.
Converse: _________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Inverse: ____________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Contrapositive:_______________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
38. If you live in Austin, then you live in Texas.
Converse: _________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Inverse: ____________________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Contrapositive:_______________________________________________________________________
T or F If false, give a counterexample: ______________________________________________________
Identify as either Inductive or Deductive Reasoning.
Give the conclusion, then tell if each fits the Law of Syllogism or the Law of Detachment.
I or D
D or S
_____ 39. Every time you don’t do the review assignment, you do poorly on the next test.
_____
You didn’t do all of the review assignment. Conclusion: _________________________________
_____ 40. If you come in for tutoring, you understand more completely the concepts.
D or S _____
If you understand more completely the concepts, you will pass the test.
If you come in for tutoring, you can conclude that:___________________________________
41.
EF bisects < DEG. If m<DEF = 4 ( 3x – 4 ) and m<FEG = 4 ( x + 4 )
Write and equation, solve for x, and then find m < DEF, m < FEG, and m < DEG.
_____
_____
_____
_____
42. Point F is between E and G. Draw a diagram, label, and find and solve for , then find all the segments
lengths if EF = 5 ( x + 2 ), FG = 2 x , and EG = 12 x
_____
_____
_____
_____
43. Determine if each conditional is true. If false, give a counterexample.
a. If
b. If
c.
, then
, then
.
.
If angles are congruent, then the angles are vertical angles.
d. If an angle is greater than 90, then the angle is an obtuse angle.
44. In the picture below, m < DEF = 2( x + 5 ) , m < FEG = 3 x + 10 , and m < DEG = 80
Write and equation, solve for x, and then find m < DEF, m < FEG, and m < DEG.
_____
_____
_____
_____
45. Twice the complement of an angle is the same as the supplement of the angle decreased by 32.
Find the measure of the angle, the measure of the complement, and the measure of the supplement.
Show an equation and all work or no credit!
_____ = the angle
_____ = the complement
_____ = the supplement
Solve each of these equations, and give the reason for each step!
46. ________________________________________
3 x + 18 = 6 x – 24
47. ________________________________________
x + 9 = 6 ( x – 3 ) – 2x