How do you prove a shape is a rhombus with coordinates?

To prove that it is a rhombus, remember that the definition of a rhombus is a quadrilateral with four congruent sides. Therefore, to prove it is a rhombus you must verify that all sides are the same length. You can use the distance formula or the Pythagorean Theorem to do this.

How do you prove that the diagonals of a square are perpendicular?

The diagonals of a square are perpendicular bisectors of one another. As a result, Their intersection forms four right angles, and each diagonal is split into two congruent pieces. Therefore, if given the length of a diagonal, the length of one segment of that diagonal is half of the length of the entire diagonal.

How do you prove a parallelogram is a rhombus using diagonals?

If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). If the diagonals of a parallelogram are perpendicular, then it’s a rhombus (neither the reverse of the definition nor the converse of a property).

How do you prove that a rhombus is a square?

1) If all four interior angles equal 90 degrees , the rhombus must be a square. 2) If the diagonals are equal , then the rhombus must be a square.

How do you prove coordinates?

The coordinate proof is a proof of a geometric theorem which uses “generalized” points on the Cartesian Plane to make an argument. The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .

How do you prove a square?

Proving that a Quadrilateral is a Square If the quadrilateral is a rectangle with two consecutive sides congruent, then it is a square. If the quadrilateral is a rectangle with perpendicular diagonals, then it is a square. If the quadrilateral is a rhombus one of whose angles is a right angle, then it is a square.

How do you know if a square is perpendicular?

The diagonals of a square intersect (cross) in a 90 degree angle. This means that the diagonals of a square are perpendicular.