Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel and equal opposite sides. In Grade 6 Saxon Math Course 1 (Chapter 7: Fractions and Geometric Concepts), students learn its properties: opposite sides are equal in length, opposite angles are equal, and consecutive angles are supplementary (sum to 180 degrees). Special types include the rhombus (all four sides equal), rectangle (all angles 90 degrees), and square (all sides equal and all right angles). The area of a parallelogram equals base times perpendicular height (A = bh), not base times slant side.
Key Concepts
Property A parallelogram is a quadrilateral with two pairs of parallel sides. Special types include the rhombus (equal sides), rectangle (right angles), and square (equal sides and right angles).
Examples A shape with side lengths $5, 8, 5, 8$ and opposite sides parallel is a parallelogram. A parallelogram with four $90^\circ$ angles is a rectangle. A parallelogram with four equal sides of length 7 and four $90^\circ$ angles is a square.
Explanation Think of a parallelogram as the parent of a shape family! It’s a tilted rectangle. If you make its sides equal, you get a rhombus. If you straighten its corners to 90 degrees, you get a rectangle. Do both, and you have the super special square! Every square is both a rectangle and a rhombus, making it the overachiever of the family.
Common Questions
What is a parallelogram?
A parallelogram is a quadrilateral with two pairs of parallel sides. Opposite sides are equal in length and opposite angles are equal.
What are the properties of a parallelogram?
Opposite sides are parallel and equal. Opposite angles are equal. Consecutive angles add to 180 degrees. Diagonals bisect each other.
How is a rectangle a special parallelogram?
A rectangle is a parallelogram where all four angles are 90 degrees. Its opposite sides are still parallel and equal.
What is the area formula for a parallelogram?
A = base x height, where height is the perpendicular distance between the parallel bases, not the slant side.
Find the area of a parallelogram with base 12 cm and perpendicular height 7 cm.
A = 12 x 7 = 84 cm squared.