To analyze the statements made by Shawndra and Marcella, we need to consider the properties of quadrilaterals, specifically trapezoids, rectangles, and squares.
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Definitions:
- A trapezoid (or trapezium in some regions) is defined as a quadrilateral with at least one pair of parallel sides.
- A rectangle is a quadrilateral that has four right angles.
- A square is a rectangle with all sides of equal length.
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Shawndra's Statements:
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First Statement: "It is not possible to draw a trapezoid that is a rectangle."
- This statement is correct. A rectangle has two pairs of parallel sides and all right angles, which conforms to the definition of a rectangle. However, a trapezoid, by definition, only needs one pair of parallel sides and doesn't require right angles. While all rectangles can be seen as special types of trapezoids (specifically, those with properties of parallel sides and right angles), not all trapezoids can be rectangles unless they meet the perpendicular requirement for angles. Thus, not every trapezoid can qualify as a rectangle.
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Second Statement: "It is possible to draw a square that is a rectangle."
- This statement is also correct. A square is indeed a specific type of rectangle because it possesses all the properties of a rectangle (four right angles) and additionally has all four sides of equal length. Therefore, squares are included in the broader category of rectangles.
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Marcella's Statements:
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First Statement: "It is possible to draw a trapezoid that is a rectangle."
- This statement is incorrect in the literal sense of saying that a trapezoid can be drawn such that it adheres to the exact properties of a rectangle without configuration. While it is true that rectangles are a subset of trapezoids, one cannot simply draw a shape that is a trapezoid (with one pair of parallel sides) that can be inherently a rectangle unless it matches both conditions (which particular trapezoid shapes do not naturally qualify as).
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Second Statement: "It is possible to draw a square that is a rectangle."
- This statement is correct as previously mentioned.
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Conclusion:
Shawndra is correct regarding the first statement about trapezoids not being rectangles, but both she and Marcella are correct about squares being rectangles. Marcella's claim about "a trapezoid that is a rectangle" is the only one that is misleading or incorrect in strict terms.
In summary:
- Shawndra is correct about trapezoids not being able to be rectangles in the specific sense described.
- Both are correct about squares being rectangles.