Quadrilaterals on the Coordinate Plane

Front

What is a quadrilateral?

Back

A quadrilateral is a polygon with four sides, four vertices, and four angles.

Front

What are the properties of a parallelogram?

Back

A parallelogram has opposite sides that are equal in length, opposite angles that are equal, and adjacent angles that are supplementary.

Front

How can you determine if two lines are parallel using the slope formula?

Back

Two lines are parallel if their slopes are equal.

Front

What is the distance formula?

Back

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

Front

What is the slope formula?

Back

The slope formula is used to find the slope (m) of a line given two points (x1, y1) and (x2, y2): m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1, meaning their slopes are opposite reciprocals.

Front

How can you prove that a quadrilateral is a rectangle?

Back

A quadrilateral is a rectangle if it has four right angles or if the diagonals are equal in length.

Front

What is the midpoint formula?

Back

The midpoint formula is used to find the midpoint M between two points (x1, y1) and (x2, y2): M = ((x1 + x2)/2, (y1 + y2)/2).

Front

What is the formula for the area of a parallelogram?

Back

The area A of a parallelogram is given by A = base × height.

Front

How can you show that the diagonals of a parallelogram bisect each other?

Back

You can show that the diagonals of a parallelogram bisect each other by proving that the midpoints of the diagonals are the same.