Parallelogram
A parallelogram is a quadrilateral with two pairs of parallel sides in Grade 8 Saxon Math Course 3. Students study the properties of parallelograms including congruent opposite sides, congruent opposite angles, and bisecting diagonals, and calculate area using the formula base times height. Understanding parallelograms supports work with all related quadrilaterals including rectangles, rhombuses, and squares.
Key Concepts
Property A quadrilateral with two pairs of parallel sides is called a parallelogram.
Examples A rhombus is a parallelogram where all four sides are equal in length. A square is a parallelogram where all sides are equal and all angles are $90^\circ$. A rectangle is a parallelogram where all angles are $90^\circ$.
Explanation Think of a rectangle that got a little push. A parallelogram has two sets of parallel sides, which means opposite sides are always equal in length, and opposite angles are always identical. This balanced setup makes it the parent shape for other cool quadrilaterals like squares, rectangles, and rhombuses, which are all just fancy parallelograms with extra rules.
Common Questions
What is a parallelogram in 8th grade geometry?
A parallelogram is a quadrilateral with two pairs of opposite sides that are parallel and equal in length. Rectangles, rhombuses, and squares are all special types of parallelograms.
What are the properties of a parallelogram?
In a parallelogram: opposite sides are parallel and congruent, opposite angles are congruent, consecutive angles are supplementary, and diagonals bisect each other.
How do you find the area of a parallelogram?
Area = base times height, where the height is the perpendicular distance between the two parallel bases. Note that the height is not the slant side length.
What is the difference between a parallelogram and a rectangle?
A rectangle is a special parallelogram where all four angles are right angles. All rectangles are parallelograms, but not all parallelograms are rectangles.
How is the parallelogram covered in Saxon Math Course 3?
Saxon Math Course 3 covers parallelogram properties, area calculation, and uses parallelograms as a foundation for deriving area formulas for triangles and trapezoids.