It is not true that if a polygon is a quadrilateral, then it is a square. While all squares are quadrilaterals, not all quadrilaterals are squares. In fact, a square is just one specific type of quadrilateral.
To understand this, let’s first define what a quadrilateral is. A quadrilateral is a polygon with four sides. This definition is broad and encompasses various shapes, including squares, rectangles, parallelograms, trapezoids, and rhombuses.
Now, let’s explore some of these other types of quadrilaterals to see why they are not squares.
– A rectangle is a quadrilateral with four right angles. While a square is a special type of rectangle, not all rectangles are squares. Rectangles can have sides of different lengths, whereas squares have all sides equal in length.
– A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. Again, a square is a specific type of parallelogram with all sides equal and right angles, but not all parallelograms are squares.
– A trapezoid is a quadrilateral with at least one pair of parallel sides. Trapezoids can have sides of different lengths and angles that are not necessarily right angles. Therefore, they are not squares.
– A rhombus is a quadrilateral with all sides equal in length. While a rhombus may seem similar to a square, it does not necessarily have right angles. So, while all squares are rhombuses, not all rhombuses are squares.
A square is a specific type of quadrilateral that has four equal sides and four right angles. However, not all quadrilaterals share these properties, so it is not true that if a polygon is a quadrilateral, then it is a square.