Question

matching 3 points. for the statement if a polygon has 6 sides, then it is a hexagon, identify the following: converse, inverse, contrapositive. if a polygon has 6 sides, then it is not a hexagon. if a polygon is a hexagon, then it has 6 sides. if a polygon does not have 6 sides, then it is not a hexagon. if a polygon does not have 6 sides, then it is a hexagon. if a polygon is not a hexagon, then it does not have 6 sides.

Explanation:

Let the original statement be "If \(p\) (a polygon has 6 sides), then \(q\) (it is a hexagon)". The converse is "If \(q\), then \(p\)", the inverse is "If not \(p\), then not \(q\)", and the contra - positive is "If not \(q\), then not \(p\)".

• Converse: If a polygon is a hexagon, then it has 6 sides.
• Inverse: If a polygon does not have 6 sides, then it is not a hexagon.
• Contra - positive: If a polygon is not a hexagon, then it does not have 6 sides.

Answer:

Converse: If a polygon is a hexagon, then it has 6 sides.
Inverse: If a polygon does not have 6 sides, then it is not a hexagon.
Contra - positive: If a polygon is not a hexagon, then it does not have 6 sides.