Definition of a Parallelogram
The definition of a parallelogram is a Grade 6 geometry concept in Reveal Math, Course 1. A parallelogram is a quadrilateral with two pairs of opposite parallel sides. Both pairs of opposite sides are also equal in length, and both pairs of opposite angles are equal. Rectangles, rhombuses, and squares are all special types of parallelograms. The height of a parallelogram is the perpendicular distance between the two bases, not the slant side, and this distinction is critical when applying the area formula A = base x height.
Key Concepts
Property A parallelogram is a four sided shape (quadrilateral) with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal in measure.
Examples A square is a special parallelogram with four equal sides and four 90° angles. A rhombus with a side length of 5 is a parallelogram where all four sides are equal, but the angles may not be 90°. A standard rectangle is also a parallelogram because its opposite sides are parallel.
Explanation Think of a rectangle that's been pushed over! Its opposite sides stay parallel and equal, but the angles aren't necessarily perfect right angles anymore. It's a shape that loves to lean while keeping its opposite sides perfectly aligned, just like a disciplined dancer mid pose.
Common Questions
What is a parallelogram?
A parallelogram is a quadrilateral (4-sided polygon) with two pairs of parallel opposite sides. Opposite sides are equal in length and opposite angles are equal. The pairs of parallel sides never meet.
What special quadrilaterals are parallelograms?
Rectangles (4 right angles), rhombuses (4 equal sides), and squares (4 equal sides and 4 right angles) are all special parallelograms. Every square is a rhombus; every rectangle and rhombus is a parallelogram.
What is the height of a parallelogram?
The height is the perpendicular distance between the base and the opposite side, measured at a 90-degree angle. It is not the length of the slant side, which is always longer.
How is a parallelogram different from a trapezoid?
A parallelogram has two pairs of parallel sides. A trapezoid (exclusive definition) has exactly one pair of parallel sides. Parallelograms are a subset of quadrilaterals, distinct from trapezoids.
Do opposite sides of a parallelogram have to be equal?
Yes. In any parallelogram, both pairs of opposite sides are equal in length. This is a property that follows from the definition of two pairs of parallel sides.
When do students learn the definition of a parallelogram?
Parallelogram properties are introduced in Grade 6 geometry in Reveal Math, Course 1, as part of the area and polygon unit.
Which textbook covers the definition of a parallelogram?
Reveal Math, Course 1, used in Grade 6, covers parallelogram definition and properties in the geometry chapter.