Mason drew a quadrilateral in which all four sides are the same length and the opposite angles have the same measures. This description fits the following types of quadrilaterals:
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Rhombus: It has all sides of equal length and opposite angles that are equal.
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Square: A square is a specific type of rhombus where all angles are right angles. It also meets the condition of having all four sides equal and opposite angles equal.
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Parallelogram: While a parallelogram generally has opposite sides that are equal and opposite angles that are equal, the specific description that all sides are equal and opposite angles are equal still identifies the rhombus and squares as specific types of parallelograms.
Therefore, the correct selections would be:
- Rhombus
- Square
- Parallelogram
(Note: A rectangle does not fit the description since it doesn't require all sides to be equal, and a trapezoid is not applicable as it is defined by having only one pair of parallel sides.)