To determine if a polygon is a square, Allie can utilize the following statements:
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If it is a rectangle with 4 sides of equal length, then it must be a square.
- This statement is true because a rectangle with all sides equal is, by definition, a square.
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If it is a parallelogram with 4 right angles, then it must be a square.
- This statement is also true because a parallelogram with all right angles must have opposite sides equal, and if all sides are equal as well, it is a square.
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If it is a rhombus with 4 right angles, then it must be a square.
- This statement is true as well. A rhombus has all sides of equal length, and if it also has right angles, it qualifies as a square.
The other statements are not valid:
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If it is a quadrilateral with 4 sides of equal length, then it must be a square.
- This statement is false because a quadrilateral can have 4 equal sides but not necessarily have right angles (e.g., a rhombus does not have to be a square).
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If it is a quadrilateral with exactly 1 pair of parallel sides, then it must be a square.
- This statement is false because having one pair of parallel sides indicates it could be a trapezoid, which is not a square.
So the correct statements that Allie can use to determine if the polygon is a square are:
- If it is a rectangle with 4 sides of equal length, then it must be a square.
- If it is a parallelogram with 4 right angles, then it must be a square.
- If it is a rhombus with 4 right angles, then it must be a square.
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