Question

question 1-37
which statement is the inverse of the following conditional (\if-then\) statement?
if two angles are vertical angles, then they are congruent.

○ if two angles are congruent, then they are right angles.
○ if two angles are congruent, then they are vertical angles.
○ if two angles are not vertical angles, then they are not congruent.
○ if two angles are not congruent, then they are not vertical angles.

Explanation:

To find the inverse of a conditional statement \( p \to q \) (where \( p \) is the hypothesis and \( q \) is the conclusion), we negate both the hypothesis and the conclusion. The inverse is \(
eg p \to
eg q \).

Step 1: Identify \( p \) and \( q \) in the original statement

The original statement is "If two angles are vertical angles, then they are congruent." Here, \( p \): "two angles are vertical angles" and \( q \): "they are congruent."

Step 2: Negate \( p \) and \( q \)

Negating \( p \): "two angles are not vertical angles"
Negating \( q \): "they are not congruent"

Step 3: Form the inverse statement

Using the negated \( p \) and \( q \), the inverse statement is "If two angles are not vertical angles, then they are not congruent."

Answer:

The option "If two angles are not vertical angles, then they are not congruent." (the third option among the given choices)