Question

which statement is the converse of the following conditional? if a polygon has three sides, then it is a triangle. a. if a polygon does not have three sides, then it is not a triangle. b. if a polygon is not a triangle, then it does not have three sides. c. if a polygon is a triangle, then it does not have three sides. d. if a polygon is a triangle, then it has three sides.

Explanation:

To find the converse of a conditional statement "If \( p \), then \( q \)", we switch the hypothesis (\( p \)) and the conclusion (\( q \)).

The given conditional statement is: "If a polygon has three sides, then it is a triangle." Here, \( p \) is "a polygon has three sides" and \( q \) is "it is a triangle."

Step 1: Identify \( p \) and \( q \)

• \( p \): A polygon has three sides
• \( q \): It is a triangle

Step 2: Form the converse

The converse of "If \( p \), then \( q \)" is "If \( q \), then \( p \)". Substituting the values of \( p \) and \( q \), we get: "If a polygon is a triangle, then it has three sides."

Now let's analyze the options:

• Option A: This is the contrapositive (negating both and switching), not the converse.
• Option B: This is also not the converse (it's a misstatement of the inverse or contrapositive).
• Option C: This is incorrect as it contradicts the original statement.
• Option D: Matches the converse we derived.

Answer:

D. If a polygon is a triangle, then it has three sides.