Question
Decide if the following biconditional statement is true or false: A polygon is a quadrilateral if and only if it has four sides. False
Ask by Martinez Osborne. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The statement is true.
Solution
To determine the truth of the biconditional statement "A polygon is a quadrilateral if and only if it has four sides," we need to analyze both directions of the statement:
1. **If a polygon is a quadrilateral, then it has four sides.**
- This part is true because, by definition, a quadrilateral is a polygon with exactly four sides.
2. **If a polygon has four sides, then it is a quadrilateral.**
- This part is also true because any polygon that has four sides is classified as a quadrilateral.
Since both directions of the biconditional statement are true, the overall statement is true.
Therefore, the statement "A polygon is a quadrilateral if and only if it has four sides" is **true**, not false.
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Simplify this solution Beyond the Answer
Ah, the intriguing world of polygons! In fact, the biconditional statement you encounter is true! A polygon is indeed a quadrilateral if and only if it has exactly four sides. This classification is fundamental in geometry, where each type of polygon is defined by the number of sides it has. To dive a little deeper, think of quadrilaterals as a party where the guest list is exclusive to shapes with four sides—like squares, rectangles, and trapezoids. If a shape has four sides, it's definitely on the list, and if it's attending, it's categorized as a quadrilateral. So, next time you see a four-sided shape, you can confidently classify it as a quadrilateral!
