Here are the correct answers to each of your questions along with explanations for why they are correct:
Question 1
Which is an example of a conditional statement?
Correct Answer: If two angles add up to 90 degrees, then they are complementary angles.
Why it’s correct:
A conditional statement is expressed in the form "If P, then Q," where P is a hypothesis and Q is a conclusion. This statement fits the format and clearly presents a condition about angle relationships.
Question 2
If both the conditional statement and its converse are true, the statements can be combined to be written as a/an _______.
Correct Answer: Biconditional Statement
Why it’s correct:
A biconditional statement combines a conditional statement and its converse, typically phrased "P if and only if Q." This indicates that both statements are true.
Question 3
The sentence "Triangles have three sides." is an example of a _________.
Correct Answer: Postulate / Definition
Why it’s correct:
This statement defines a fundamental property of triangles and does not fit the conditional structure; it serves as a basic definition in geometry.
Question 1 (Follow-up)
Which of the following is a converse of the statement?
Correct Answer: If two angles are congruent, then they are both 25 degrees.
Why it’s correct:
The converse of a conditional statement "If P, then Q" is formed by swapping P and Q. Here, the original statement was "If two angles are both 25 degrees (P), then they are congruent angles (Q)."
Question 2 (Follow-up)
Which of the following is an inverse of the statement?
Correct Answer: If two angles are not 25 degrees, then they are not congruent angles.
Why it’s correct:
The inverse of "If P, then Q" is "If not P, then not Q." Therefore, if we negate the original hypothesis and conclusion, we derive this statement.
Question 3 (Follow-up)
Which of the following is a contrapositive of the statement?
Correct Answer: If two angles are not congruent angles, then they cannot both be 25 degrees.
Why it’s correct:
The contrapositive of "If P, then Q" is "If not Q, then not P." Here, negating the original statement gives us this correct answer.
Question 1 (Venn Diagram)
Write a conditional statement for this Venn diagram.
Correct Answer: If it is red, then it is a color.
Why it’s correct:
This is a standard conditional statement, reflecting the relationship shown in a Venn diagram where red is included in the broader category of colors.
Question 2 (Counterexample)
Write a counterexample for the converse.
Correct Answer: Blue is a color.
Why it’s correct:
If the converse states "If it is a color, then it is red," then blue serves as a counterexample because it disproves the notion that only red qualifies as a color.
Question 1 (About the Library)
Draw a conclusion for the statement if possible.
Correct Answer: The library is not closed.
Why it’s correct:
The original conditional states "If it is Monday, then the library is closed." Since the statement mentions today is Tuesday, this does not satisfy the condition, leading us to the conclusion that the library is not closed.
Question 2 (Coins)
Draw a conclusion for the statement if possible.
Correct Answer: It is not possible to draw a conclusion.
Why it’s correct:
The statements provided do not establish a direct relationship or transitive conclusion between the conditions, making it impossible to infer additional information beyond what is given.