Parallelograms

Definition

A parallelogram is a quadrilateral with opposite sides that are both parallel and equal in length. Its opposite angles are also equal.

5 Must Know Facts For Your Next Test

1. The area of a parallelogram can be calculated using the formula $Area = base \\times height$.
2. In a parallelogram, the vector representing one side plus the vector representing the adjacent side forms the diagonal of the parallelogram.
3. The dot product can be used to find angles between vectors forming a parallelogram.
4. A parallelogram's diagonals bisect each other, which can be proven using vector addition.
5. The cross product of two vectors forming adjacent sides of a parallelogram gives the area of the parallelogram.

Review Questions

• How do you calculate the area of a parallelogram using vectors?
• What is the relationship between the diagonals in a parallelogram?
• Explain how to use the dot product to find angles within a parallelogram.

Related terms

Vector: A quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another.

Cross Product: An operation on two vectors that results in another vector perpendicular to both, often used to determine areas and volumes.

Dot Product: \(A \cdot B = |A| |B| \cos{\theta}\), where \(\theta\) is the angle between vectors A and B. It measures how much one vector extends in the direction of another.