__How to prove a quadrilateral is a parallelogram__

To prove a quadrilateral is parallelogram, demonstrate that the opposite sides are congruent. To do this you will need to do the distance formula 4 times. After you are done doing the distance formula 4 times, you can write something like this:

“The quadrilateral is a parallelogram because the opposite sides are congruent”.

__How to prove a quadrilateral is a rhombus__

To prove a quadrilateral is rhombus you must first prove the quadrilateral is a parallelogram (See how to prove a parallelogram above). Then demonstrate that all the sides are congruent. To do this, you will need to do the distance formula 4 times. After you are done doing the distance formula 4 times, you can write something like this:

“The quadrilateral is a rhombus because it’s a parallelogram with all congruent sides”.

__How to prove a quadrilateral is a rectangle__

To prove a quadrilateral is a rectangle you must first prove the quadrilateral is a parallelogram (See how to prove a parallelogram). Then demonstrate that the diagonals are congruent. To do this, you will need to do the distance formula 6 times (4 because of the sides and 2 for the diagonals). After you are done doing the distance formula 6 times, you can write something like this:

“The quadrilateral is a rectangle because it’s a parallelogram with congruent diagonals”.

__How to prove a quadrilateral is a square__

To prove a quadrilateral is a square you must prove that the quadrilateral is a parallelogram, rhombus and a rectangle (See all of the above). To do this, you will need to do the distance formula 6 times (4 because of the sides and 2 for the diagonals). After you are done doing the distance formula 6 times you can write something like this:

“The quadrilateral is a square because it’s a parallelogram with all congruent sides and congruent diagonals”.