Naming a Quadrilateral

Distance Formula:

-Find distances of all sides.
a. Trapezoid- If one pair opposite sides congruent.
Isosceles trapezoid- If the diagonals are congruent.

b. Parallelogram- If opposite sides congruent.
Rhombus- If all sides congruent.
Rectangle- If diagonals are congruent.
Square- If both rhombus & rectangle.

Slope:

-Find slope of all sides.
a. Trapezoid- If one pair of opposite sides has the same slope.
b. Parallelogram- If opposite sides have same slope and are parallel.
Rectangle- If consecutive sides have opposite reciprocals and multiply to be -1 (this makes sides perpendicular).

-Find slope of diagonals.

Rhombus-If the diagonals are opposite reciprocals and multiply to be -1 (making them perpendicular. In addition, the quadrilateral had to be a parallelogram.
Square-If the quadrilateral was both a rectangle and a rhombus.

Midpoint:

-Find midpoint of diagonals.
Parallelogram- If midpoint is same, meaning that the diagonals bisect each other.
Rhombus- If a parallelogram with diagonals bisected.
-Use slope or distance formula to finish.

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