choose the sentence that shows the converse of the statement: \if a polygon has 3 congruent sides, then it is an equilateral triangle.\ if a polygon is an equilateral triangle, then it has 3 congruent sides. if an equilateral triangle has 3 congruent sides, then it is a polygon. if a polygon is an equilateral triangle, then it may not have 3 congruent sides. if it has 3 congruent sides, then an equilateral triangle is a polygon. if a polygon has 3 congruent sides, then it may not be an equilateral triangle.

Question

choose the sentence that shows the converse of the statement: \if a polygon has 3 congruent sides, then it is an equilateral triangle.\  if a polygon is an equilateral triangle, then it has 3 congruent sides.  if an equilateral triangle has 3 congruent sides, then it is a polygon.  if a polygon is an equilateral triangle, then it may not have 3 congruent sides.  if it has 3 congruent sides, then an equilateral triangle is a polygon.  if a polygon has 3 congruent sides, then it may not be an equilateral triangle.

Accepted Answer

# Brief Explanations:
To find the converse of a conditional statement "If $ p $, then $ q $", we swap the hypothesis ($ p $) and the conclusion ($ q $). The original statement is "If a polygon has 3 congruent sides ($ p $), then it is an equilateral triangle ($ q $)". Swapping $ p $ and $ q $ gives "If a polygon is an equilateral triangle ($ q $), then it has 3 congruent sides ($ p $)", which matches the first option. The other options either misinterpret the hypothesis/conclusion or introduce incorrect logic.
# Answer:
A. If a polygon is an equilateral triangle, then it has 3 congruent sides.

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