Is a rectangle a parallelogram? Yes or No? Why?
The correct answer and explanation is:
Yes, a rectangle is a parallelogram.
This is because a rectangle meets all the essential criteria of a parallelogram. A parallelogram is defined as a quadrilateral with opposite sides that are parallel and equal in length. A rectangle, by definition, is a quadrilateral in which all angles are 90 degrees.
In addition to having opposite sides that are parallel and equal in length, which makes a rectangle a parallelogram, the rectangle also has right angles at each corner. The right angles do not change the fact that the opposite sides are still parallel and equal, which are the key properties of a parallelogram. The fact that the angles are 90 degrees is an extra constraint that specifically characterizes a rectangle.
Therefore, while all rectangles are parallelograms due to the parallel and equal sides, not all parallelograms are rectangles. The main distinction is that rectangles have right angles, whereas other parallelograms can have non-right angles but still maintain the parallel and equal-length side properties.
In conclusion, every rectangle is indeed a parallelogram because it satisfies all the conditions of a parallelogram with the additional feature of right angles. But remember, the reverse is not true—parallelograms do not necessarily have right angles.