25. 4 Coordinate Proof Using Distance with Quadrilaterals

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 fourth vertex of a parallelogram given three vertices?

Back

To find the fourth vertex, use the midpoint formula or the properties of parallelograms, ensuring that opposite sides are equal and parallel.

Front

What is the distance formula?

Back

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

Front

How many times should we use the distance formula to determine if a quadrilateral is a parallelogram?

Back

You should use the distance formula 4 times to check the lengths of all four sides.

Front

What are the properties of a rectangle?

Back

A rectangle is a parallelogram with four right angles and opposite sides that are equal in length.

Front

What are the properties of a rhombus?

Back

A rhombus is a parallelogram with all four sides equal in length and opposite angles equal.

Front

What are the properties of a square?

Back

A square is a parallelogram that is both a rectangle and a rhombus, having all sides equal and all angles right angles.

Front

How can you determine if a quadrilateral is a rectangle using its diagonals?

Back

If the diagonals of a quadrilateral are equal in length, then the quadrilateral is a rectangle.

Front

What is the significance of the diagonals in a parallelogram?

Back

In a parallelogram, the diagonals bisect each other, and their lengths can help determine the type of parallelogram.

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).