Parallelograms

Front

What is a parallelogram?

Back

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

Front

What are the properties of a parallelogram?

Back

1. Opposite sides are equal in length. 2. Opposite angles are equal. 3. The diagonals bisect each other.

Front

How do you determine if a quadrilateral is a parallelogram using slopes?

Back

If both pairs of opposite sides have the same slope, then the quadrilateral is a parallelogram.

Front

What is the slope formula?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1).

Front

If the coordinates of a quadrilateral are K(2, 7), L(6, 12), M(13, 13), N(9, 8), what is the slope of KL?

Back

The slope of KL is (12 - 7) / (6 - 2) = 5/4.

Front

Back

x = 5, since opposite angles in a parallelogram are equal.

Front

How do you find the length of a side in a parallelogram?

Back

Front

If AC = 8x - 14 and EC = 2x + 11, how do you solve for x?

Back

Set AC equal to EC: 8x - 14 = 2x + 11, then solve for x.

Front

What is the distance formula?

Back

Front

If D(-5, -6), E(5, 2), F(4, -4), G(-6, -12), how do you determine if DEFG is a parallelogram?

Back

Calculate the slopes and distances of opposite sides; if they are equal, DEFG is a parallelogram.