Question

1. triangles are polygons.

conditional statement:
is it true?
converse statement:
is it true?
inverse statement:
is it true?
contrapositive statement:
is it true?

Explanation:

• Conditional statement: A conditional statement is in the form "If \(p\), then \(q\)". Here, \(p\) is "a figure is a triangle" and \(q\) is "a figure is a polygon". By definition, a triangle (a three - sided closed figure) is a type of polygon (a closed figure with straight sides).
• Converse statement: The converse of "If \(p\), then \(q\)" is "If \(q\), then \(p\)". A polygon can have more than three sides (e.g., quadrilaterals, pentagons). So, just because a figure is a polygon does not mean it is a triangle.
• Inverse statement: The inverse of "If \(p\), then \(q\)" is "If not \(p\), then not \(q\)". There are polygons that are not triangles (e.g., rectangles). So, the fact that a figure is not a triangle does not imply it is not a polygon.
• Contrapositive statement: The contrapositive of "If \(p\), then \(q\)" is "If not \(q\), then not \(p\)". If a figure is not a polygon (i.e., it does not have straight sides and is not closed), then it cannot be a triangle (since a triangle is a polygon).

Answer:

• Conditional statement: If a figure is a triangle, then it is a polygon. Is it true? Yes.
• Converse statement: If a figure is a polygon, then it is a triangle. Is it true? No.
• Inverse statement: If a figure is not a triangle, then it is not a polygon. Is it true? No.
• Contrapositive statement: If a figure is not a polygon, then it is not a triangle. Is it true? Yes.