Which shape is a quadrilateral and a rectangle? A. Rhombus B. Parallelogram C. Square D. Trapezoid
The Correct Answer and Explanation is:
Correct Answer: C. Square
A square is a geometric shape that meets the criteria of both a quadrilateral and a rectangle.
A quadrilateral is any polygon with four sides. All of the options provided — rhombus, parallelogram, square, and trapezoid — are quadrilaterals because they each have four sides.
A rectangle is a special type of quadrilateral. It has the following specific properties:
- Four right angles (each measuring 90 degrees)
- Opposite sides that are equal and parallel
Now let us examine each choice:
- A. Rhombus: A rhombus is a quadrilateral with all four sides equal in length, and opposite sides parallel. However, it does not necessarily have four right angles, so not all rhombuses are rectangles. Therefore, a rhombus is not always a rectangle.
- B. Parallelogram: A parallelogram has opposite sides that are equal and parallel, and opposite angles are equal. But like the rhombus, a parallelogram does not always have four right angles. So, not all parallelograms are rectangles.
- C. Square: A square has four sides of equal length, four right angles, and opposite sides that are parallel. These properties satisfy the definition of both a rectangle (because it has four right angles and equal opposite sides) and a quadrilateral (because it has four sides). Hence, a square is both a quadrilateral and a rectangle.
- D. Trapezoid: A trapezoid (called a trapezium in some regions) has only one pair of parallel sides. It does not require four right angles and is not defined by having equal opposite sides. Therefore, a trapezoid is not a rectangle.
In conclusion, a square fits both categories: it is a quadrilateral and also a rectangle because it meets all required properties of both shapes.
