True or False: a trapezoid is a quadrilateral, but it is not a parallelogram. Explain your thinking
True. A trapezoid is indeed a quadrilateral, but it is not a parallelogram.
To understand why, let's break it down:
1. Quadrilateral: A quadrilateral is a polygon with exactly four sides. Any shape with four sides qualifies as a quadrilateral, including trapezoids.
2. Trapezoid: A trapezoid is a specific type of quadrilateral, characterized by having only one pair of parallel sides. The other two sides are non-parallel and can have any length. This arrangement is what distinguishes a trapezoid from other quadrilaterals.
3. Parallelogram: A parallelogram, on the other hand, is a quadrilateral with two pairs of parallel sides. Both pairs of opposite sides are parallel and equal in length. This means that all angles in a parallelogram are also congruent.
Since a trapezoid only has one pair of parallel sides and does not satisfy the criteria for having two parallel pairs, it does not meet the definition of a parallelogram. Therefore, the statement is true: a trapezoid is a quadrilateral but not a parallelogram.
What are the definitions of these two terms?
http://www.mathsisfun.com/geometry/parallelogram.html
http://www.mathsisfun.com/geometry/trapezoid.html