To determine who is correct, let's analyze Shawndra's and Marcella's statements regarding the properties of quadrilaterals, specifically trapezoids, rectangles, and squares.
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Shawndra's Statements:
- "It is not possible to draw a trapezoid that is a rectangle."
- "It is possible to draw a square that is a rectangle."
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Marcella's Statements:
- "It is possible to draw a trapezoid that is a rectangle."
- "It is possible to draw a square that is a rectangle."
Analyzing the Statements
Trapezoids and Rectangles:
- A trapezoid (or trapezium in some regions) is defined primarily as a quadrilateral with at least one pair of parallel sides.
- A rectangle is defined as a quadrilateral with four right angles and opposite sides that are equal in length.
Key Points:
- A rectangle has two pairs of parallel sides (the opposite sides).
- Since a rectangle satisfies the criteria of being a quadrilateral and having at least one pair of parallel sides, it can technically also be classified as a special type of trapezoid.
However, if we strictly interpret "a trapezoid that is a rectangle," it implies that a trapezoid cannot only be "one pair of parallel sides." Therefore, Shawndra's statement that "It is not possible to draw a trapezoid that is a rectangle" aligns with common interpretations, as a rectangle would also inherently include two pairs of parallel sides.
Squares and Rectangles:
- A square is defined as a quadrilateral that has four equal sides and four right angles.
- By definition, a square meets all the criteria of a rectangle (four right angles and opposite sides equal) and therefore can be considered a rectangle.
Thus, Shawndra's statement, "It is possible to draw a square that is a rectangle," is also true.
Marcella's Statements:
- Marcella claims that "It is possible to draw a trapezoid that is a rectangle." This statement relies on the understanding that a rectangle can indeed be a special case of a trapezoid. Thus, while technically true, it isn’t nuanced and could potentially mislead because not every trapezoid is a rectangle.
- Marcella's second statement, "It is possible to draw a square that is a rectangle," is true, similar to Shawndra's.
Conclusion:
- Correctness regarding Trapezoids and Rectangles: Shawndra has a stronger argument based on the conventional definitions of trapezoids and rectangles.
- Both Shawndra and Marcella are correct in their discussions about squares being rectangles. However, Shawndra is more precise when discussing trapezoids.
In summary, while Marcella's statement about trapezoids may be considered technically correct due to the broad classification, it lacks the clarity that Shawndra provides. Therefore, Shawndra's understanding of the properties of quadrilaterals is clearer and more accurate within the context provided.
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