1. Problems to study for the chapter 2 exam
Chapter 2 REVIEW
Problems to study for the chapter 2 exam

2. 1. Based on the pattern, what are the next two terms of the sequence?,
9 630 , ,
9 630 , 9 635
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3. The correct answer is C because you are multiplying the denominator by 5 every time.
9 625 ∙ 1 5 = ∙ 1 5 =

4. 2. What conjecture can you make about the fourteenth figure in this pattern?
The fourteenth figure in the pattern is
There is not enough information.
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5. The fourteenth figure in the pattern is .1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
The fourteenth figure in the pattern is

6. 3. What is a counterexample for the conjecture
3. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8. 24 40 12 26
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7. 24 is divisible by 4 and 8 40 is divisible by 4 and 8
3. What is a counterexample for the conjecture? Conjecture: Any number that is divisible by 4 is also divisible by 8.
24 is divisible by 4 and 8
40 is divisible by 4 and 8
12 is divisible by 4 but NOT 8
26 is NOT divisible by 4 or 8
CORRECT ANSWER IS C

8. 4. What is the conclusion of the following conditional
4. What is the conclusion of the following conditional? A number is divisible by 2 if the number is even.
The sum of the digits of the number is divisible by 2.
If a number is even, then the number is divisible by 2.
The number is even.
The number is divisible by 2.
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9. A number is divisible by 2 if the number is even.
The hypothesis follows the “if” -- the number is even
The conclusion follows the “then” since there is not one in this case the then is at the beginning -- A number is divisible by 2
Correct answer is D The number is divisible by 2.

10. 5. Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular.
Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles.
Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.
Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles.
Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular.
2-2

11. If two lines intersect at right angles, then the two lines are perpendicular.
The hypothesis follows the “if” -- two lines intersect at right angles
The conclusion follows the “then” -- the two lines are perpendicular
Correct answer is B Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.

12. 6. What are the converse, inverse, and contrapositive of the following true conditional? What are the truth values of each? If a statement is false, give a counterexample. If a figure is a rhombus, then it is a parallelogram.
CONDITIONAL:
If a figure is a rhombus, then it is a parallelogram. True.
CONVERSE:
If a figure is a parallelogram, then it is a rhombus.
False − rectangle.
INVERSE:
If a figure is not a rhombus, then it is not a parallelogram.
False - rectangle.
CONTRAPOSITIVE:
If a figure is not a parallelogram, then it is not a rhombus.
True
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Non-Response Grid

13. 7. What is the converse of the following conditional
7. What is the converse of the following conditional? If a point is in the fourth quadrant, then its coordinates are negative.
If a point is in the fourth quadrant, then its coordinates are negative.
If a point is not in the fourth quadrant, then the coordinates of the point are not negative
If the coordinates of a point are not negative, then the point is not in the fourth quadrant.
If the coordinates of a point are negative, then the point is in the fourth quadrant.
2-2

14. If a point is in the fourth quadrant, then its coordinates are negative.
The hypothesis follows the “if” -- a point is in the fourth quadrant
The conclusion follows the “then” -- its coordinates are negative.
The converse switches the if and then so the correct answer is If the coordinates of a point are negative, then the point is in the fourth quadrant.

15. 8. Is the following definition of poodle reversible
8. Is the following definition of poodle reversible? If yes, write it as a true biconditional. A poodle is a dog.
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The reverse is false.
The reverse is true. An animal is a dog if (and only if) it is a poodle.
The reverse is true. An animal is a mammal if (and only if) it is a poodle.
The reverse is true. If an animal is a dog, then it is a poodle.

16. A poodle is a dog. Conditional
If something is a poodle, then it is a dog.
TRUE
Converse
If something is a dog, then it is a poodle.
FALSE
So it is not reversible. The correct answer is A.

17. 2-3 If x2 = 49, then x = 7. True; x2 = 49 if and only if x = 7.
9. For the following true conditional statement, write the converse. If the converse is also true, combine the statements as a biconditional. If x = 7, then x2 = 49.
2-3
If x2 = 49, then x = 7. True; x2 = 49 if and only if x = 7.
If x2 = 49, then x = 7. True; x = 7 if and only if x2 = 49.
If x2 = 49, then x = 7. False
If x2 = 7, then x = 49. False

18. If x = 7, then x2 = 49. Converse If x2 = 49, then x = 7. FALSE x = -7.
Since converse is FALSE cannot be written as a biconditional so the answer is C
If x2 = 49, then x = 7. False

19. 10. Which biconditional is NOT a good definition?
A whole number is even if and only if it is divisible by 2.
A whole number is odd if and only if the number is not divisible by 2.
An angle is straight if and only if its measure is 180.
A ray is a bisector of an angle if and only if it splits the angle into two angles.
2-3

20. Which biconditional is NOT a good definition?
A. A whole number is even if and only if it is divisible by 2.
True statement because even numbers are always divisible by 2.
B. A whole number is odd if and only if the number is not divisible by 2.
True statement because odd numbers are never divisible by 2.
C. An angle is straight if and only if its measure is 180.
True statement straight angle by definition is 180 degrees.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.
False statement a bisector must split the angle into two congruent angles. So the correct answer is D.

21. 2-4 𝑚∠𝐸 + 𝑚∠𝐹 = 180 ∠𝐸 is congruent to ∠𝐹 ∠𝐸 ≇∠𝐹 𝑚∠𝐸 + 𝑚∠𝐹 = 90
11. Use the Law of Detachment to draw a conclusion from the two given statements. If two angles are complementary, then the sum of their measures is 90°. ∠E and ∠F are complementary.
2-4
𝑚∠𝐸 + 𝑚∠𝐹 = 180
∠𝐸 is congruent to ∠𝐹
∠𝐸 ≇∠𝐹
𝑚∠𝐸 + 𝑚∠𝐹 = 90

22. If two angles are complementary, then the sum of their measures is 90°
If two angles are complementary, then the sum of their measures is 90°. ∠E and ∠F are complementary.
The Law of Detachment can be applied if you are given the hypothesis of a true conditional then you can assume the conclusion.
∠E and ∠F are complementary is the hypothesis so you can conclude that the sum of their measures is 90 degrees.
The correct answer is D. 𝑚∠𝐸 + 𝑚∠𝐹 = 90

23. 12. Use the Law of Syllogism to draw a conclusion from the two given statements. If you exercise regularly, then you have a healthy body. If you have a healthy body, then you have more energy.
If you do not have more energy, then you do not exercise regularly.
You have more energy.
You have a healthy body.
If you exercise regularly, then you have more energy.
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24. If you exercise regularly, then you have a healthy body
If you exercise regularly, then you have a healthy body. If you have a healthy body, then you have more energy.
The Law of Syllogism allows you to skip what they have in common if the then of one is the if of the other. If you exercise regularly, then you have a healthy body. If you have a healthy body, then you have more energy. They link so you can skip over “you have a healthy body”. The correct answer is D. If you exercise regularly, then you have more energy.

25. 2-4 If it is Friday night, then Josef is wearing his school colors.
13. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the three given statements. If it is Friday night, then there is a football game. If there is a football game, then Josef is wearing his school colors. It is Friday night.
If it is Friday night, then Josef is wearing his school colors.
Josef is wearing his school colors.
There is a football game.
If it is not Friday night, then Josef is not wearing his school colors.
2-4

26. If it is Friday night, then there is a football game
If it is Friday night, then there is a football game. If there is a football game, then Josef is wearing his school colors. It is Friday night.
Reorder them to link:
It is Friday night.
If it is Friday night, then there is a football game. If there is a football game, then Josef is wearing his school colors.
Since we know it is Friday night, Josef is wearing his school colors.
Correct answer is B.

27. 14. 𝐵𝐷 bisects ∠𝐴𝐵𝐶. 𝑚∠𝐴𝐵𝐶 = 7x. 𝑚∠𝐴𝐵𝐷=3𝑥+36. Find 𝑚∠𝐷𝐵𝐶.
108 72
180
252
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28. 𝐵𝐷 bisects ∠𝐴𝐵𝐶. 𝑚∠𝐴𝐵𝐶 = 7x. 𝑚∠𝐴𝐵𝐷=3𝑥+36. Find 𝑚∠𝐷𝐵𝐶.A D 7x
3x + 36 B C
7𝑥=3𝑥+36+3𝑥+36 Because it bisects ∠𝐴𝐵𝐶
7𝑥=6𝑥+72
𝑥=72 =
216+36=
252
Correct answer is D.

29. 15. Name the Property of Equality that justifies this statement:
15. Name the Property of Equality that justifies this statement: If l = m, then m = l .
Multiplication Property of Equality
Symmetric Property of Equality
Subtraction Property of Equality
Transitive Property of Equality
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30. If l = m, then m = l . Switching about the equals sign is the
Symmetric Property of Equality.
The correct answer is B.

31. 16. Name the Property of Congruence that justifies this statement: If ∠A ≌ ∠B and ∠B ≌ ∠C , then ∠A ≌ ∠C .
Transitive Property of Congruence
Symmetric Property of Congruence
Reflexive Property of Congruence
None of these
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32. If ∠A ≌ ∠B and ∠B ≌ ∠C , then ∠A ≌ ∠C .
When you can link the if then like the Law of Syllogism the property is:
Transitive Property of Congruence
The correct answer is A.

33. 17. Complete the two-column proof.
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a. Given; b. Substitution Property; c. Addition Property of =; d. Division Property of =; e. Symmetric Property of =.
a. Given; b. Substitution Property; c. Addition Property of =; d. Addition Property of =; e. Symmetric Property of =.
a. Given; b. Symmetric Property of =; c. Addition Property of =; d. Division Property of =; e. Reflexive Property of =.
a. Given; b. Substitution Property; c. Addition Property of =; d. Division Property of =; e. Reflexive Property of =.

34. Given
Substitution
Addition Property of =
Division Property of =
Symmetric Property of =

35. 18. Complete the paragraph proof.
2-6
180
180
m∠3 ∠3
(c) Transitive Property of =

36. 19. Find the values of x and y.
2-6
x = 15, y = 17
x = 112, y = 68
x = 68, y = 112
x = 17, y = 15

37. 7𝑥+7=112 Vertical Angles Theorem
7𝑥=105 Subtraction Property of =
𝑥=15 Division Property of =
4𝑦+112=180 Linear Pair Postulate
4𝑦=68 Subtraction Property of =
𝑦=17 Division Property of =
Correct Answer is A.

38. 20. Complete the two-column proof.
2-6
Given
Substitution
Property of =
Vertical Angles Theorem
Transitive