Question

1. given the statement.

if a shape has exactly three sides, then it is a triangle.
match the alternate forms to their classifications.
draggable item → category
if a shape is not a triangle, then it does not have exactly three sides. → converse
if a shape does not have exactly three sides, then it is not a triangle. → inverse
if a shape is a triangle, then it has exactly three sides. → contrapositive

Explanation:

• Contrapositive: Negates and swaps the hypothesis and conclusion of the original statement ("If \(

eg q \), then \(
eg p \)" for original "If \( p \), then \( q \)"). Here, original \( p \): "has exactly three sides", \( q \): "is a triangle"; contrapositive is \(
eg q \to
eg p \).

• Inverse: Negates both the hypothesis and conclusion of the original statement ("If \(

eg p \), then \(
eg q \)").

• Converse: Swaps the hypothesis and conclusion of the original statement ("If \( q \), then \( p \)").

Answer:

1. "If a shape is not a triangle, then it does not have exactly three sides." → contrapositive
2. "If a shape does not have exactly three sides, then it is not a triangle." → inverse
3. "If a shape is a triangle, then it has exactly three sides." → converse