Is the following statement a true biconditional?
A polygon is a square (if and only if) a polygon has four congruent sides.
Yes, the statement "A polygon is a square if and only if a polygon has four congruent sides" is a true biconditional.
To determine whether the statement "A polygon is a square if and only if a polygon has four congruent sides" is a true biconditional, we need to evaluate if both parts of the statement are true.
First, let's break down the statement:
- "A polygon is a square": This means that any polygon being referred to is specifically a square.
- "A polygon has four congruent sides": This means that the polygon being referred to has four sides that are all equal in length.
Now, let's evaluate each part:
- If a polygon is a square, then it does have four congruent sides. This is true because a square is defined as a quadrilateral with all sides equal in length.
- If a polygon has four congruent sides, it can be a square, but it can also be a rhombus (a quadrilateral with all sides equal in length but opposite angles not necessarily equal). Therefore, this part of the statement is not entirely correct.
Given that one part of the statement is true, while the other part is not entirely true, we can conclude that the statement "A polygon is a square if and only if a polygon has four congruent sides" is not a true biconditional.