Which statement is true?
All quadrilaterals are rectangles.
All parallelograms are rectangles.
All squares are rectangles.
All rectangles are squares.
The correct answer and explanation is:
The correct statement is: All squares are rectangles.
Explanation:
A rectangle is defined as a quadrilateral with four right angles, meaning all its internal angles are 90 degrees. A square is a special type of rectangle that not only has four right angles but also has all four sides of equal length. Therefore, every square is a rectangle because it meets the definition of having four right angles.
However, the reverse is not true. While every square is a rectangle, not all rectangles are squares. For a rectangle to be a square, all its sides must be of equal length. Rectangles can have different side lengths, so a rectangle with unequal sides is not a square.
Now, let’s look at the other options:
- All quadrilaterals are rectangles: This is false. A quadrilateral is any four-sided polygon, and it can take many forms. While rectangles are quadrilaterals, not all quadrilaterals have four right angles, as required for a rectangle. For example, a trapezoid or a rhombus is a quadrilateral but not a rectangle.
- All parallelograms are rectangles: This is false. A parallelogram is a quadrilateral where opposite sides are parallel, but the angles are not necessarily 90 degrees. Rectangles are a specific type of parallelogram where all angles are right angles. Not all parallelograms have this property. For example, a rhombus is a parallelogram but not a rectangle.
- All rectangles are squares: This is false. While all squares are rectangles, not all rectangles are squares. A rectangle can have unequal adjacent sides, which would disqualify it from being a square.
In summary, the correct answer is that all squares are rectangles, but not all rectangles are squares.