The true statement is: a) all rectangles are quadrilaterals.
Explanation: A rectangle is defined as a quadrilateral with four right angles. By definition, a quadrilateral is a polygon with four sides. Therefore, every rectangle meets the criteria to be classified as a quadrilateral. However, not all quadrilaterals are rectangles, because a quadrilateral can have sides and angles of various lengths and measures, which do not conform to the properties of a rectangle. The other options are incorrect because:
- b) Not all quadrilaterals are rectangles. There are many types of quadrilaterals, such as trapezoids and rhombuses, that do not qualify as rectangles.
- c) Not all quadrilaterals are parallelograms. Parallelograms are special types of quadrilaterals where opposite sides are parallel and equal in length, but not all quadrilaterals share this property.
- d) Not all quadrilaterals are squares. A square is a specific type of rectangle with all sides equal, but many quadrilaterals do not have this property.