Question 1

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A)


Which is an example of a conditional statement?

(1 point)
Responses

The angles of triangles add up to 180 degrees.
The angles of triangles add up to 180 degrees.

Vertical angles are always congruent
Vertical angles are always congruent

If two angles add up to 90 degrees, then they are complementary angles.
If two angles add up to 90 degrees, then they are complementary angles.

Today is Tuesday if and only if yesterday was Monday.
Today is Tuesday if and only if yesterday was Monday.
B)If both the conditional statement and its converse are true, the statements can be combined to be written as a/an _______(1 point)
Responses

Biconditional Statement
Biconditional Statement

Contrapositive
Contrapositive

Inverse
Inverse

They cannot be combined.
They cannot be combined.
C)The sentence "Triangles have three sides." is an example of a _________(1 point)
Responses

Conditional Statement
Conditional Statement

Postulate / Definition
Postulate / Definition

Biconditional Statement
Biconditional Statement

Contrapositive
Contrapositive
Question 2
A)
For the following questions, use the statement below.

If two angles are both 25 degrees, then they are congruent angles.



Which of the following is a converse of the statement?

(1 point)
Responses

If two angles are not 25 degrees, then they are not congruent angles.
If two angles are not 25 degrees, then they are not congruent angles.

If two angles are congruent, then they are both 25 degrees.
If two angles are congruent, then they are both 25 degrees.

If two angles are not congruent angles, then they cannot both be 25 degrees.
If two angles are not congruent angles, then they cannot both be 25 degrees.

None of the above.
None of the above.
B)


Which of the following is an inverse of the statement?

(1 point)
Responses

If two angles are not 25 degrees, then they are not congruent angles.
If two angles are not 25 degrees, then they are not congruent angles.

If two angles are congruent, they are both 25 degrees.
If two angles are congruent, they are both 25 degrees.

If two angles are not congruent angles, then they cannot both be 25 degrees.
If two angles are not congruent angles, then they cannot both be 25 degrees.

None of the above.
None of the above.
C)Which of the following is a contrapositive of the statement?(1 point)
Responses

If two angles are not 25 degrees, then they are not congruent angles.
If two angles are not 25 degrees, then they are not congruent angles.

If two angles are congruent, they are both 25 degrees.
If two angles are congruent, they are both 25 degrees.

If two angles are not congruent angles, then they cannot both be 25 degrees.
If two angles are not congruent angles, then they cannot both be 25 degrees.

None of the above.
None of the above.
Question 3
A)
Write a conditional statement for this Venn diagram.

(1 point)
Responses

Red is a color
Red is a color

It is red, if and only if it is a color.
It is red, if and only if it is a color.

If it is red, then is is a color.
If it is red, then is is a color.

All colors are red.
All colors are red.
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B)Write a counterexample for the converse.(1 point)
Responses

Blue is a color.
Blue is a color.

Red is also a flavor of Gatorade.
Red is also a flavor of Gatorade.

Red is not a color.
Red is not a color.

There is no counterexample, because the converse is also true.
There is no counterexample, because the converse is also true.
Question 4
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A)
Draw a conclusion for the statement if possible.



If it is Monday, then the library is closed. Today is Tuesday

(1 point)
Responses

The library is closed
The library is closed

The library is not closed
The library is not closed

The library is neither open nor closed.
The library is neither open nor closed.

It is not possible to draw a conclusion.
It is not possible to draw a conclusion.
B)
Draw a conclusion for the statement if possible.



If a coin is a quarter, then it is worth 25 cents. If a coin is worth 25 cents, then 4 would make a dollar.

(1 point)
Responses

If I have a coin, then I have a quarter.
If I have a coin, then I have a quarter.

If a coin is a quarter, then 4 would make a dollar.
If a coin is a quarter, then 4 would make a dollar.

If it is worth 25 cents, it is a coin.
If it is worth 25 cents, it is a coin.

It is not possible to draw a conclusion.

1 answer

Certainly! Here are the answers to your questions from each section:

Question 1:

A) Which is an example of a conditional statement?
Response: If two angles add up to 90 degrees, then they are complementary angles.

B) If both the conditional statement and its converse are true, the statements can be combined to be written as a/an _______
Response: Biconditional Statement

C) The sentence "Triangles have three sides." is an example of a _________
Response: Postulate / Definition


Question 2:

A) Which of the following is a converse of the statement?
Response: If two angles are congruent, then they are both 25 degrees.

B) Which of the following is an inverse of the statement?
Response: If two angles are not 25 degrees, then they are not congruent angles.

C) Which of the following is a contrapositive of the statement?
Response: If two angles are not congruent angles, then they cannot both be 25 degrees.


Question 3:

A) Write a conditional statement for this Venn diagram.
Response: If it is red, then it is a color.

B) Write a counterexample for the converse.
Response: Blue is a color.


Question 4:

A) Draw a conclusion for the statement if possible.
If it is Monday, then the library is closed. Today is Tuesday.
Response: It is not possible to draw a conclusion.

B) Draw a conclusion for the statement if possible.
If a coin is a quarter, then it is worth 25 cents. If a coin is worth 25 cents, then 4 would make a dollar.
Response: It is not possible to draw a conclusion.


Feel free to ask if you need further clarification or additional help!