Coordinate Plane Proofs of Parallelograms

Front

What is a parallelogram?

Back

A parallelogram is a four-sided figure (quadrilateral) with opposite sides that are parallel and equal in length.

Front

How do you find the slope of a line given two points?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does it mean if two lines have the same slope?

Back

If two lines have the same slope, they are parallel to each other.

Front

What is the distance formula?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) and is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of slopes in parallelograms?

Back

In parallelograms, opposite sides have equal slopes, indicating they are parallel.

Front

If the slopes of two sides of a quadrilateral are negative reciprocals, what does this indicate?

Back

It indicates that the two sides are perpendicular to each other.

Front

What is the relationship between the slopes of sides AB and DC in a parallelogram?

Back

The slopes of sides AB and DC are equal, indicating that they are parallel.

Front

How can you prove that a quadrilateral is a parallelogram using slopes?

Back

If both pairs of opposite sides have equal slopes, then the quadrilateral is a parallelogram.

Front

What does it mean if two sides of a parallelogram are congruent?

Back

It means that the two sides have the same length.

Front

What is the definition of a rectangle?

Back

A rectangle is a parallelogram with four right angles.