Proving Parallelograms in the Coordinate Plane

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 prove that a quadrilateral is a parallelogram using slopes?

Back

To prove a quadrilateral is a parallelogram, show that both pairs of opposite sides have the same slope.

Front

What is the distance formula?

Back

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

Front

How many times do you need to use the slope formula to prove a parallelogram?

Back

You need to use the slope formula 2 times, once for each pair of opposite sides.

Front

How many times do you need to use the distance formula to prove a parallelogram?

Back

You need to use the distance formula 2 times, once for each pair of opposite sides.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y over the change in x (rise/run).

Front

If two lines have the same slope, what can be said about them?

Back

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

Front

What is the midpoint formula?

Back

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

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

How do you find the value of x in a rectangle?

Back

In a rectangle, opposite sides are equal. Use this property to set up an equation and solve for x.