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Name ___________________________
Chapter 2 Logic & Proof Test Review
Rewrite the following statements as a conditional, then state the hypothesis and conclusion.
1. Whenever I think about home, I get misty-eyed.
Conditional __________________________________________________________________
Hypothesis: __________________________Conclusion ____________________________
2. If it rains tomorrow, then I will use my umbrella.
Converse___________________________________________________________
Inverse_____________________________________________________________
Contrapositive________________________________________________________
3. If m A = 90°, then A is a right angle.
T or F Converse____________________________________________________________
T or F Inverse______________________________________________________________
T of F Contrapositive_________________________________________________________
4. Write a true conditional statement from the following: Monday is a weekday.
______________________________________________________________________.
Use inductive reasoning to complete the following patterns (5-7):
5. 3, 7, 11, 15, ______
6.
7. -3, 6, -12, 24, _____
______, ______
make a conjecture about this pattern ________________________
_____________________________________________________
8. Complete the conjecture “The product of two negative numbers is ______________________”.
Determine if the each conjecture is true. If not write a counterexample for each (9-11).
9. If 2x + 3 = 15, then x = 6. _____________________________________________
10. If BD bisects <ABC, then m<ABD = m<CBD.____________________________________
11. If n is an integer, then –n is positive.____________________________________________
12.
Rewrite the statements so that they are in a logical order and reach a conclusion.
a. If Suzie Shopper gets fat, then her dress will not fit.
b. If Suzie Shopper eats too much, then she will get fat.
c. If Suzie Shopper needs a new dress, then she will go to dinner at a nice restaurant.
d. If her dress does not fit, then Suzie Shopper will need to exercise.
e. If Suzie Shopper goes to the store, then Suzie will buy shoes.
f. If Suzie Shopper buys shoes, then Suzie Shopper will need a new dress.
g. If Suzie goes to dinner at a nice restaurant, then Suzie Shopper will eat too much.
Correct order: State the letters only. __________________________
Conclusion: _____________________________________________________________________
13. Determine if the conjecture is valid by the Law of Syllogism:
Given: If you fly from Texas to California, you travel from the central to the Pacific time zone.
If you travel from the central to the Pacific time zone, then you gain two hours.
Conjecture: If you fly from Texas to California, then you gain two hours.
Valid or invalid ?
14. Determine if the conjecture is valid by the Law of Detachment:
Given: If you want to go on a field trip, you must have a signed permission slip.
Sophie has a signed permission slip.
Conjecture: Sophie wants to go on a field trip.
Valid or invalid ?
Rewrite each definition or statement as a biconditional (15-16).
15. A triangle with no sides equal is a scalene triangle.___________________________________
16. A circle is a set of points in a plane a given distance from the center.______________________
17. Logic Puzzle: It is a three-digit odd number. It is less than 200. Each of the digits is different.
The sum of its digits is 17. The ones digit is greater than 7. The number is __________
18. Three little pigs, who each lived in a different type of house, handed out treats for Halloween.
Use the clues to figure out which pig lived in each house and what type of treat each pig
handed out.
A. Petey Pig did not hand out popcorn.
B. Pippin Pig does not live the wood house.
C. The pig that lives in the straw house, handed out popcorn.
D. Petunia Pig handed out apples
E. The pig who handed out chocolate, does not live in the brick house.
19. The five things that can be used as reasons in a proof are:
20. If the pattern indicated below is continued, what would be the total number of cubes in the next
stage of the pattern?
Answers: 1. If I think about home, then I will get misty-eyed. H-I think about home C-I will get misty-eyed. 2. Con-If I use my umbrella, then it will rain
tomorrow. In-If it doesn’t rain tomorrow, then I won’t use my umbrella. Cont-If I don’t use my umbrella, then it won’t rain tomorrow. 3. Con-If <A is a right,
angle, then m<A=90. True In- If m<A≠90, then <A is not a right angle. True Cont- If <A is not a right angle, then m<A≠90. True 4. If it is Monday, then it is
a weekday. 5. 19 6. , 7-sided figure 7. -48 ; each term is double the previous term with alternating signs. 8. Positive 9. True 10. True 11. If n=4, then -4
is not positive. 12. e,f,c,g,b,a,d ; If Suzie Shopper goes to the store, then she will need to exercise. 13. Valid 14. Invalid 15. A triangle is scalene if and only if
it has no equal sides. 16. A set of points in a plane is a circle if and only if they are a given distance from the center. 17. 179 18. Petey, chocolate-wood; Pippin,
popcorn-straw; Petunia,apples-brick 19. Definitions, postulates, theorems, given, algebra properties 20. 64 21. e,a,b,c 22. B,d,e,c,a,c 23.b,c,e,d,a,c
Justifications: 1. Segment add. 2. Def.midpoint 3. Def. midpoint 4. Def.  <s 5. Transitive prop. 6. Subtraction prop. 7. Def.supplementary <s 8. Reflexive prop.
9. Angle add. Post. 10. Symmetric prop. 11. Def. vertical <s 12. Def.compl.<s 13. Transitive prop. 14. Substitution prop. 15. Def. midpt. 16.def. supple.<s
17. Def. right < 18. Def.obtuse< 19. Reflexive prop. 20. All right <s are  21. Def.  <s 22.transitive prop. 23. Subtraction prop. 24. Segment add. 25. All right
<s  26. Def. right < 27. Division 28. Def. obtuse < 29. Def. angle bisector 30. Linear pr. Th. 31. Distributive prop. 32. Division prop. 33. Addition prop.
Proofs:
Complete each proof using the choices below each 2-column proof (some may be used more
than once) :
21.
Statements
Reasons
3n + 25 = 9n -5
25 = 6n - 5
30 = 6n
5=n
a. subtraction
b. addition
c. division
d. multiplication
e. given
f. substitution
22.
Given: 2  3
Prove:  1 and  3 are supplementary
1
2
Statements
3
Reasons
2  3
m2  m3
 1 and  2 are supplementary
m  1 + m  2 =180º
m  1 + m  3 =180º
 1 and  3 are supplementary
a. substitution
b. given
c. definition of supplementary angles
d. definition of congruent angles
e. linear pair theorem
f. reflexive property
23.
Given:  1 and  2 are complementary
Prove:  2 and  3 are complementary
1
2
3
Statements
 1 and  2 are complementary
m  1 + m  2 =90º
1  3
m1  m3
m  3 + m  2 =90º
 2 and  3 are complementary
a. substitution
b. given
c. definition of complementary angles
d. definition of congruent angles
e. vertical angles theorem
f. reflexive property
Reasons
Justify each statement with a postulate, theorem, definition, or algebra property:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
If point X is between points C and D, then CX + XD = CD.
If point A is between C and D where CA  AD, then A is the midpoint of
CD.
If A is the midpoint of CD, then CA = ½ (CD).
If mA = mD, then A  D.
If AB  XY and XY  MP, then AB  MP.
If AB + CD = CD + XY, then AB = XY.
If 1 and 2 are supplementary, then m1 + m2 = 180.
If XY  MN, then XY  MN.
If X is in the interior of CPD, then mCPX + mXPD= mCPD.
If ABC  XYZ, then XYZ  ABC.
If XYZ and WYV are vertical angles, then XYZ  WYV.
If mA + mP = 90, then A and P are complementary.
If 2  4 and 4  7, then 2  7.
If AB + EF = CD and EF=MN, then AB + MN = CD.
If CM = MD on CD, then M is the midpoint of CD.
If mEFG + mXYZ = 180, then EFG and XYZ are supplementary.
If mABC = 90, thenABC is a right angle.
If mAPB > 90, then APB is obtuse.
ABC  ABC.
If A and B are right angles, then A  B.
If 1  2, then m1 = m2.
If m1 = m3 and m3 = m2, then m1 = m2.
If XY + QP = ST, then XY = ST – QP.
If B is between X and Y, then XB + BY= XY.
If ABC and XYZ are right angles, then ABC  XYZ.
If ABC is a right angle, then mABC = 90.
If 3(AB)= 3(BC), then AB = BC.
If mCXA = 140, then CXA is an obtuse angle.
If X is in the interior of JKL such that JKX  XKL, then KX is an
angle bisector.
If 3 and 4 form a linear pair, then m3 + m4 = 180.
If 6(x – 10) = 360, then 6x – 60 = 360.
If 6x = 360, then x = 60.
If 13y – 10 =29, then 13y = 39.