Definition of a Parallelogram
A parallelogram is a four-sided figure (quadrilateral) where opposite sides are parallel and equal in length, and opposite angles are equal in measure. Rectangles, squares, and rhombuses are all special types of parallelograms. A rectangle is a parallelogram with four right angles; a rhombus has all four sides equal. Understanding this definition, taught in Reveal Math, Course 1, Module 8, is essential for knowing when to apply the area formula A = bh in 6th grade geometry.
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 in geometry?
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length and opposite angles are equal in measure.
Is a rectangle a parallelogram?
Yes. A rectangle has two pairs of parallel sides and equal opposite sides, so it is a parallelogram. It is a special parallelogram where all angles are 90 degrees.
Is a square a parallelogram?
Yes. A square is a special parallelogram where all four sides are equal and all four angles are 90 degrees. It is also a special rectangle and a special rhombus.
What makes a rhombus a special parallelogram?
A rhombus is a parallelogram where all four sides are equal in length, but the angles are not necessarily 90 degrees.
How is a parallelogram different from a rectangle?
A rectangle is a special parallelogram with four 90-degree angles. A general parallelogram has slanted sides and angles that are not necessarily 90 degrees.
When do 6th graders learn the definition of a parallelogram?
This is covered in Module 8 of Reveal Math, Course 1, as part of the area unit.