Parallelogram vs. Trapezoid
Distinguishing parallelograms from trapezoids depends on counting pairs of parallel sides. In Grade 6 Saxon Math Course 1, a parallelogram has two pairs of parallel opposite sides; a trapezoid has exactly one pair. Rectangles, rhombuses, and squares are all special parallelograms. In a trapezoid, the two parallel sides are called bases and the non-parallel sides are called legs. This classification is central to the quadrilateral strand in middle school geometry.
Key Concepts
Property A parallelogram is a quadrilateral with two pairs of parallel sides. A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Examples A quadrilateral with one pair of parallel sides, like bases of length 4 and 10, is a trapezoid. A rectangle is a parallelogram because its opposite sides are parallel, but it is not a trapezoid. A shape with no parallel sides, like a standard kite, cannot be a parallelogram or a trapezoid.
Explanation It's all about parallel lines! A parallelogram is like a box that got pushed over—both pairs of opposite sides stay parallel no matter what. A trapezoid is different; it’s like a section of a pyramid. Only one pair of sides (usually the top and bottom) are parallel, while the other two sides are on a collision course if you extend them.
Common Questions
What is the key difference between a parallelogram and a trapezoid?
A parallelogram has two pairs of parallel sides; a trapezoid has exactly one pair of parallel sides.
Is a rectangle a parallelogram?
Yes — a rectangle has two pairs of parallel sides and four right angles, making it a special parallelogram.
What are the parallel sides of a trapezoid called?
The two parallel sides of a trapezoid are called bases; the non-parallel sides are called legs.
Can a shape be both a parallelogram and a trapezoid?
Under the exclusive definition used in Saxon Math, no. A trapezoid has exactly one pair, so a parallelogram (with two pairs) does not qualify.
How do you identify a parallelogram from a figure?
Check that both pairs of opposite sides are parallel. Opposite sides will also be equal in length.