Download Chapter 2 Test Review Period ______ # 1

Geometry
Chapter 2 Test Review
Name ___________________________
Period _______
# 1 – 25: Write the vocabulary term that fits the definition.
1. the part p of a conditional statement following the word if
2. statement formed by negating the hypothesis and conclusion [~p  ~q]
3. of statement p is “not p,” written as ~p; the negation of a true statement is false and the
negation of a false statement is true; we use these to write related conditional statements
4. a statement that can be written in the form “if p, then q”
5. a statement can have this value of true (T) or false (F)
6. the part q of a conditional statement following the word then
7. statement formed by exchanging the hypothesis and conclusion [q  p]
8. an example that proves that a conjecture or statement is false; a drawing, a statement or a number
9. statement formed by both exchanging and negating the hypothesis and conclusion [~q  ~p]
10. a statement that describes a mathematical object and can be written as a true biconditional
11. 4-sided polygon
12. a 3-sided polygon
13. the process of using logic to draw conclusions from given facts, definitions & properties
14. a statement that can be written in the form “p if and only if q” or “if p, then q” and “if q, then p.”
15. related conditional statements that have the same truth value
16. a closed plane figure formed by 3 or more line segments such that each segment
intersects exactly 2 other segments only at their endpoints and no 2 segments
with a common endpoint are collinear
17. the process of reasoning that a rule or statement is true because specific cases are true
18. a statement you believe to be true based on inductive reasoning
19. uses boxes and arrows to show the structure of the proof
20. a style of proof in which the statements and reasons are presented in paragraph form
21. any statement you can prove
22. an argument that uses logic, definitions, properties, and previously proven statements to show that a
conclusion is true
23. a style of proof in which the statements are written in the left-hand column and
the reasons are written in the right-hand column
# 24 - 51: Choose the best answer. Please write in capital letters! Use the space around the edges or a separate
sheet of paper to work out some of the problems or to begin writing some of the statements, then
choose your answer.
_______ 24. Under what circumstances will the sum of three numbers always be negative?
A. when at least one number is less than zero
B. when at least one number equals zero
C. when all three numbers are less than zero
D. when one number is less than zero and the other two are greater than zero
_______ 25. Ms. Patrick wrote the fractions 0.75 , 1.5 , 3 , 6 on the board. Then she asked
1
1
1 1
Sabrina to describe the relationship among the numbers. Which statement
describes the relationship among the numbers?
A. the fractions are equivalent
B. the fractions are in ascending order
C. the fractions are in descending order
D. the fractions are doubling from left to right
_______ 26. The first five numbers of a number array are shown below.
What is the sum of the numbers in row 8?
Row 1
0
A. 176
Row 2
1 2
B. 217
Row 3
3 4 5
C. 230
Row 4
6 7 8 9
D. 252
Row 5 10 11 12 13 14
_______ 27. The depth of a pond is measured at the same location and on the same day every year for
a number of years. The table below shows the measurements. If the pattern continued, what was
the depth of the pond in 2007?
Depth of Pond
A. 10 feet
Year
Depth (in feet)
B. 8 feet
2003
30
C. 16 feet
2004
22
D. 2 feet
2005
16
2006
12
_______ 28. Beavercreek High School uses a telephone chain to notify employees of school closings and delays.
The principal calls 3 people in the first round of the telephone chain. Each of those people calls 3
other people in the second round of the telephone chain. If the pattern continues, how many
employees are called in the 4th round of the telephone chain?
A. 27
B. 81
C. 243
D. 100
_______ 29. The table below contains the results of a biology experiment. Assuming the pattern shown in the
table continues, what is the value of b?
Record of Blooms
A. 4096
B. 64
C. 1024
D. 8
Week
Number of Blooms
1
4
2
16
3
64
4
5
256 b
_______ 30. The first four rows of a number array are shown below. What number will be at the far
right end of row 7?
A. 160
B. 220
C. 290
D. 370
Row 1
Row 2
Row 3
Row 4
20
30 40
50
60 70
80 90 100 110
_______ 31. Find the next item in the pattern 4, 6, 8, 9, 10, …
A. 13
C. 15
B. 12
D. 17
_______ 32. Complete the conjecture. The sum of two even numbers is ____.
A. even
C. sometimes odd, sometimes even
B. odd
D. even most of the time
_______ 33. The table shows the estimated population at BHS 14 years and over by age and sex according to
Miss Beach’s best estimate. Make a conjecture based on the data.
Girls
Guys
Population 18 Years and Over by Age and Sex
14 to 15 years
16 to 17 years
18 years and over
1,357
1,216
503
1,234
1,183
515
A. Girls outnumbered guys in the 18 years and over population
B. Guys outnumbered girls in the 18 years and over population
C. There are more 18 years old and over in 2000 than in previous years.
D. There are fewer 18 years old and over in 2000 than in previous years.
_______ 34. Show that the conjecture is false by finding a counterexample.
If x > y, then x/y > 0.
A. x = 10, y = -4
B. x = 10, y = 4
C. x = 4, y = 10
D. x = -10, y = 4
_______ 35. Identify the hypothesis and conclusion of the conditional statement.
If it is raining and sunny, then there is a rainbow.
A. Hypothesis: It is raining and sunny.
B. Hypothesis: There is a rainbow.
C. Hypothesis: Sun makes rainbows.
D. Hypothesis: Rain and sun happen together.
Conclusion: There is a rainbow.
Conclusion: It is raining and sunny.
Conclusion: Rain does not make clouds.
Conclusion: Rain and clouds do not happen together.
_______ 36. Write a conditional statement from the statement: A dog has 4 legs.
A. If it has 4 legs, then it is a dog.
B. Every dog has 4 legs.
C. If it is a dog, then it has 4 legs.
D. It has 4 legs and it is a dog.
_______ 37. Determine if the conditional statement is true. If false, give a counterexample.
If a figure has four right angles, then it is a square.
A. True
B. False, a rectangle has 4 right angles, and it is not a square.
_______ 38. Write the converse, inverse, and contrapositive of the conditional statement.
If an animal is a cat, then it has two eyes.
A. Converse: If an animal does not have two eyes, then it is not a cat.
Inverse: If an animal is not a cat, then it does not have two eyes.
Contrapositive: If an animal has two eyes, then it is a cat.
B. Converse: All cats have two eyes.
Inverse: All animals have two eyes.
Contrapositive: All cats are animals, and animals have two eyes.
C. Converse: If an animal is not a cat, then it does not have two eyes.
Inverse: If an animal does not have two eyes, then it is not a cat.
Contrapositive: If an animal is a cat, then it has two eyes.
D. Converse: If an animal has two eyes, then it is a cat.
Inverse: If an animal is not a cat, then it does not have two eyes.
Contrapositive: If an animal does not have two eyes, then it is not a cat.
_______ 39. Determine if the conjecture is valid by the Law of Detachment.
Given: If Miss Beach makes cookies tonight, then Miss Beach must have an oven.
Miss Beach has an oven.
Conjecture: Miss Beach made cookies tonight.
A. the conjecture is valid, because we know p q is true
B. the conjecture is not valid, because we know p  q is true and p is true
C. the conjecture is valid, because we know p  q is true and p is true
D. the conjecture is not valid, because we know p  q is true and q is true
_______ 40. Determine if the conjecture is valid by the Law of Syllogism.
Given: If you are in Sarasota, then you are in Florida. If you are in Florida, then
you are in the South.
Conjecture: If you are in Sarasota, then you are in the South.
A. no, the conjecture is not valid
B. yes, the conjecture is valid.
_______ 41. Draw a conclusion from the given information.
Given: If two lines never intersect, then they are parallel.
If two lines are parallel, then they have the same slope.
Two lines never intersect.
A. Conclusion: The lines are parallel.
B. Conclusion: The lines are parallel, never intersect, and have the same slope.
C. Conclusion: The lines never intersect.
D. Conclusion: The lines have the same slope.
_______ 42. Write the conditional statement and converse within the biconditional.
biconditional: A rectangle is a square if and only if it is a rhombus.
A. Conditional: If all four sides of the rectangle are equal length, then it is a square.
Converse: If a rectangle is a square, then its four sides are equal length.
B. Conditional: If a rectangle is a square, then it is also a rhombus.
Converse: If a rectangle is a rhombus, then it is also a square.
C. Conditional: If all four sides are equal length, then all four angles are 90°.
Converse: If all four angles are 90°, then all four sides are equal length.
D. Conditional: If a rectangle is not a square, then its sides are of different lengths.
Converse: If the sides are of different lengths, then the rectangle is not a square.
_______ 43. There is a myth that a dog’s bark can be heard a mile away. A group of scientists observed a dog
in a field, and they found that the bark does travel. Therefore, the myth is true. Is the conclusion a
result of inductive or deductive reasoning?
A. Since the conclusion is based on a pattern of observation, it is a result of inductive reasoning.
B. Since the conclusion is based on a pattern of observation, it is a result of deductive reasoning.
C. Since the conclusion is based on logical reasoning from scientific research, it is a result of inductive reasoning.
D. Since the conclusion is based on logical reasoning from scientific research, it is a result of deductive reasoning.
_______ 44. For the conditional statement, write the converse and biconditional statement.
If a figure is a rectangle with sides l and w, then A = lw.
A. Converse: If a figure is not a rectangle with sides l and w, then A ≠ lw.
Biconditional: A figure is a rectangle with sides l and w if and only if A = lw.
B. Converse: If A = lw, then the figure is a rectangle with sides l and w.
Biconditional: A figure is a rectangle with sides l and w if and only if A = lw.
C. Converse: If A ≠ lw, then the figure is not a rectangle with sides l and w.
Biconditional: A figure is not a rectangle with sides l and w if and only if A ≠ lw.
D. Converse: If A ≠ lw, then the figure is not a rectangle with sides l and w.
Biconditional: A figure is a rectangle with sides l and w if and only if A = lw.
_______ 45. Determine if the biconditional is true. If false, give a counterexample.
biconditional: A figure is a square if and only if it is a quadrilateral.
A. The biconditional is true
B. The biconditional is false. A quadrilateral does not necessarily have four congruent sides and four right angles.
C. The biconditional is false. All squares are parallelograms with four 90° angles.
D. The biconditional is false. A quadrilateral does not necessarily have four 90° angles.
_______ 46. Write the definition as a biconditional.
definition: An obtuse angle is an angle whose measure is greater than 90° and less than 180°.
A. An angle is obtuse if its measure is greater than 90° and less than 180°.
B. An angle is obtuse if and only if its measure is greater than 90° and less than 180°.
C. An angle’s measure is greater than 90° and less than 180°if it is obtuse.
D. An angle is obtuse if and only if it is not acute.
_______ 47. Look at the work and solution to the equation 5x – 5 = 40. Choose the missing
justifications.
A. Substitution Property of Equality
5x – 5 = 40
Given
Division Property of Equality
+ 5 +5
B. Addition Property of Equality
Division Property of Equality
5x = 45
________?________
C. Division Property of Equality
5
5
Subtraction Property of Equality
D. Addition Property of Equality
x=9
_______?_________
Reflexive Property of Equality
_______ 48. Look at the work and solution. Choose the missing justifications.
m ABC = m ABD + m DBC
108° = (6x + 8) ° + (2x - 4) °
108 = 8x + 4
104 = 8x
13 = x
_____?_______
Substitution Property of Equality
Simplify
Substitution Property of Equality
_____?_______
A. Angle Addition Postulate
Division Property of Equality
B. Transitive Property of Equality
Division Property of Equality
C. Angle Addition Postulate
Simplify
D. Segment Addition Postulate
Multiplication Property of Equality
_______ 49. Choose the correct answers to fill in the blanks. (where you see these: ???)
Given: 1 and 2 are complementary. m 1 = 55°.
Prove: m 2 = 35°.
Statements
1. 1 and 2 are complementary
2. ???
3. m 1 + m 2 = 90°
4. 55° + m 2 = 90°
5.
m 2 = 35°
1
2
Reasons
1. Given
2. Given
3. ???
4. Substitution Property of Equality
5. ???
A. m 2 = 55°
Definition of complementary angles
Subtraction Property of Equality
B. m 1 = 55°
Definition of complementary angles
Substitution Property of Equality
C. m 1 = 35°
Definition of complementary angles
Subtraction Property of Equality
D. m 1 = 55°
Definition of complementary angles
Subtraction Property of Equality
_______ 50. Identify the property that justifies the statement.
AB = CD and CD = EF. So AB = EF.
A. Reflexive Property of Equality
B. Substitution Property of Congruence
C. Symmetric Property of Equality
D. Transitive Property of Equality
_______ 51. Look at the work and solution. Choose the missing justifications.
Given: AC = BD.
AC = BD
AC = AB + BC
BD = BC + CD
AB + BC = BC + CD
AB = CD
A
B
Given
_______?_________
Segment Addition Postulate
_______?_________
Subtraction Property of Equality
C
D
A. Segment Addition Postulate
Substitution Prop. of Equality
B. Substitution
Segment Addition Postulate
C. Segment Addition Postulate
Addition Prop. of Equality
D. Given
Substitution Prop. of Equality