FTCE Professional Education Practice Exam

Are all quadrilaterals also parallelograms?

1. True

2. False

3. Only some quadrilaterals are parallelograms

4. Only convex quadrilaterals are parallelograms

The correct answer is: False

The statement that all quadrilaterals are parallelograms is false because not every quadrilateral possesses the properties that define a parallelogram. A parallelogram is a specific type of quadrilateral characterized by having both pairs of opposite sides that are parallel and equal in length, as well as congruent opposite angles. While all parallelograms are quadrilaterals (since they have four sides), the reverse is not true: quadrilaterals include a variety of shapes, such as trapezoids and kites, that do not meet the criteria of having parallel opposite sides. For example, a rectangle and a square are types of parallelograms, while a trapezoid has only one pair of parallel sides and cannot be classified as a parallelogram. Thus, while certain subsets of quadrilaterals (like rectangles, rhombuses, and squares) are indeed parallelograms, many other quadrilaterals do not share these characteristics.