Chapter 2 Test B

1

Choose the correct converse of the if-then statement below:
If you had enough sleep, then you did well on the test.

If you did not do well on the test, then you did not get enough sleep.

If you did well on the test, then you received an "A".

If you did well on the test, then you had enough sleep.

If you did not get enough sleep, then you did not do well on the test.

1

Choose the correct inverse of the if-then statement below:
If the m\angle{X} is less than 90^o, then \angle{X} is acute.

If \angle{X} is acute, then the m\angle{X} is less than 90^o.

If \angle{X} is not acute, then the m\angle{X} is not less than 90^o.

If \angle{X} is obtuse, then m\angle{X} is not 90^o.

If m\angle{X} is not less than 90^o, then \angle{X} is not acute.

1

Choose the correct contrapositive of the if-then statement below:
If a tree is an evergreen, then it does not lose its leaves in the fall.

If a tree is not an evergreen, then it does not lose its leaves in the fall.

If a tree is not an evergreen, then it does lose its leaves in the fall.

If a tree does not lose its leaves in the fall, then it is an evergreen.

If a tree does lose its leaves in the fall, then it is not an evergreen.

1

Choose the statement below that is a TRUE biconditional.

Two angles are a linear pair if and only if they are supplementary.

Two angles are vertical if and only if they are congruent.

A polygon is regular if and only if it is equilateral.

An angle is a right angles if and only if it has a measure of 90^o.

1

Choose the statement below that CANNOT be written as a TRUE biconditional.

If two angles are complementary, then they are both acute.

If x is even, then x + 2 is even.

If a segment has a midpoint, then it is divided into two congruent segments.

If two lines intersect to form right angles, then they are perpendicular.

1

In the Show Your Work space, write or draw a counterexample:
If two angles are congruent, then they are vertical angles.

Use the pattern below to first describe the pattern, then determine the next item in the sequence.

3, -6, 12, -24, 48,...

1

Describe the pattern in words

1

What is the next number in the sequence?

Use the pattern below to first describe the pattern, then determine the next item in the sequence.

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1

Describe the pattern in words

1

What is the next item in the sequence? Draw in the Show Your Work section.

For the next 3 questions, use either the Law of Detachment or the Law of Syllogism to make a possible conclusion. If no conclusion can be reached, state NOT VALID.

2

If I get my clothes dirty, then I will have to wash them. If I have to wash them, then I will need to buy detergent.

2

If you forget your homework, then you will have to run home. If you have to run home, then you will trip and fall.

2

If you golf, then you have a country club membership. Alaina plays golf.

5

Using the Show Your Work section, solve the algebraic proof and justify each step.

For the next 14 questions, determine which property, definition, postulate, or theorem matches the statement provided. Defintions must have the word "Definition", however properties and theorems do not need their identifier.

1

If 3k + j = 40 and j = 2, then 3k + 2 = 40.

1

If AB = CD and CD = EF, then AB = EF.

1

If 2x = 40, then x = 20.

1

If m\angle{X} = m\angle{Y}, then m\angle{Y} = m\angle{X}.

1

If two lines are perpendicular, then they form right angles.

1

XY = XY

1

If m\angle{X} = 90^o, then \angle{X} is a right angle.

1

If 3k - 4 = 10, then 3k = 14.

1

If \frac{k}{4} = 20, then k = 80.

1

If m\angle{X} + m\angle{Y} = 90^o, then these angle are complementary.

1

If \angle{A} and \angle{B} are a linear pair, then they are supplementary.

1

If WX = XY and X is between W and Y, then X is the midpoint.

1

AK + KB = AB

1

If \angle{1} and \angle{2} are vertical angles, then \angle{1}\cong\angle{2}.

Complete the proof below:

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Reason #1

1

Statement #2

1

Reason #3

1

Reason #4

Complete the proof below:

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1

Reason #1

1

Reason #2

1

Reason #3

1

Reason #4

3

In the proof below, there are 3 errors. Correctly select each incorrect step and what that step should be.

Reason #2: Should be Angle Addition

Reason #2: Should be Definition of Complementary

Reason #3: Should be Definition of Congruence

Reason #4: Should be Definition of Congruence

Reason #4: Should be Substitution

Reason #5: Should be Defintion of Complementary

Reason #6: Should be Defintion of Right Angle

Reason #6: Should be Substitution

Reason #7: Should be Defintion of Right Angle

Complete the proof below:

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Reason #1

1

Reason #2

1

Reason #3

Complete the proof below:

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1

Reason #3

1

Statement #4

1

Reason #5

1

Statement #6

1

6

Using the Show Your Work section, complete the proof below:

Complete the proof below:

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1

Reason #2

1

Reason #3

1

Reason #4

1

Reason #5

BONUS:

Complete the proof below:

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Chapter 2 Test B

Choose the correct converse of the if-then statement below:If you had enough sleep, then you did well on the test.

Choose the correct inverse of the if-then statement below:If the m\angle{X} is less than 90o, then \angle{X} is acute.

Choose the correct contrapositive of the if-then statement below:If a tree is an evergreen, then it does not lose its leaves in the fall.

Choose the statement below that is a TRUE biconditional.

Choose the statement below that CANNOT be written as a TRUE biconditional.

In the Show Your Work space, write or draw a counterexample:If two angles are congruent, then they are vertical angles.

Describe the pattern in words

What is the next number in the sequence?

Describe the pattern in words

What is the next item in the sequence? Draw in the Show Your Work section.

If I get my clothes dirty, then I will have to wash them. If I have to wash them, then I will need to buy detergent.

If you forget your homework, then you will have to run home. If you have to run home, then you will trip and fall.

If you golf, then you have a country club membership. Alaina plays golf.

Using the Show Your Work section, solve the algebraic proof and justify each step.

If 3k + j = 40 and j = 2, then 3k + 2 = 40.

If AB = CD and CD = EF, then AB = EF.

If 2x = 40, then x = 20.

If m\angle{X} = m\angle{Y}, then m\angle{Y} = m\angle{X}.

If two lines are perpendicular, then they form right angles.

XY = XY

If m\angle{X} = 90o, then \angle{X} is a right angle.

If 3k - 4 = 10, then 3k = 14.

If \frac{k}{4} = 20, then k = 80.

If m\angle{X} + m\angle{Y} = 90o, then these angle are complementary.

If \angle{A} and \angle{B} are a linear pair, then they are supplementary.

If WX = XY and X is between W and Y, then X is the midpoint.

AK + KB = AB

If \angle{1} and \angle{2} are vertical angles, then \angle{1}\cong\angle{2}.

Reason #1

Statement #2

Reason #3

Reason #4

Reason #1

Reason #2

Reason #3

Reason #4

In the proof below, there are 3 errors. Correctly select each incorrect step and what that step should be.

Reason #1

Reason #2

Reason #3

Reason #3

Statement #4

Reason #5

Statement #6

Using the Show Your Work section, complete the proof below:

Reason #2

Reason #3

Reason #4

Reason #5

Reason #5

Choose the correct converse of the if-then statement below:If you had enough sleep, then you did well on the test.

Choose the correct inverse of the if-then statement below:If the m\angle{X} is less than 90o, then \angle{X} is acute.

Choose the correct contrapositive of the if-then statement below:If a tree is an evergreen, then it does not lose its leaves in the fall.

Choose the statement below that is a TRUE biconditional.

Choose the statement below that CANNOT be written as a TRUE biconditional.

In the Show Your Work space, write or draw a counterexample:If two angles are congruent, then they are vertical angles.

Describe the pattern in words

What is the next number in the sequence?

Describe the pattern in words

What is the next item in the sequence? Draw in the Show Your Work section.

If I get my clothes dirty, then I will have to wash them. If I have to wash them, then I will need to buy detergent.

If you forget your homework, then you will have to run home. If you have to run home, then you will trip and fall.

If you golf, then you have a country club membership. Alaina plays golf.

Using the Show Your Work section, solve the algebraic proof and justify each step.

If 3k + j = 40 and j = 2, then 3k + 2 = 40.

If AB = CD and CD = EF, then AB = EF.

If 2x = 40, then x = 20.

If m\angle{X} = m\angle{Y}, then m\angle{Y} = m\angle{X}.

If two lines are perpendicular, then they form right angles.

XY = XY

If m\angle{X} = 90o, then \angle{X} is a right angle.

If 3k - 4 = 10, then 3k = 14.

If \frac{k}{4} = 20, then k = 80.

If m\angle{X} + m\angle{Y} = 90o, then these angle are complementary.

If \angle{A} and \angle{B} are a linear pair, then they are supplementary.

If WX = XY and X is between W and Y, then X is the midpoint.

AK + KB = AB

If \angle{1} and \angle{2} are vertical angles, then \angle{1}\cong\angle{2}.

Choose the correct converse of the if-then statement below:
If you had enough sleep, then you did well on the test.

Choose the correct inverse of the if-then statement below:
If the m\angle{X} is less than 90^o, then \angle{X} is acute.

Choose the correct contrapositive of the if-then statement below:
If a tree is an evergreen, then it does not lose its leaves in the fall.

In the Show Your Work space, write or draw a counterexample:
If two angles are congruent, then they are vertical angles.

If m\angle{X} = 90^o, then \angle{X} is a right angle.

If m\angle{X} + m\angle{Y} = 90^o, then these angle are complementary.

Choose the correct converse of the if-then statement below:
If you had enough sleep, then you did well on the test.

Choose the correct inverse of the if-then statement below:
If the m\angle{X} is less than 90^o, then \angle{X} is acute.

Choose the correct contrapositive of the if-then statement below:
If a tree is an evergreen, then it does not lose its leaves in the fall.

In the Show Your Work space, write or draw a counterexample:
If two angles are congruent, then they are vertical angles.

If m\angle{X} = 90^o, then \angle{X} is a right angle.

If m\angle{X} + m\angle{Y} = 90^o, then these angle are complementary.