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Coord. Proof Tools

Learn which tools are used to prove which properties.

To prove...You use...
Two sides (or diagonals) congruent, the distance formula and show that both sides (or diagonals) have the same length.
Two sides are parallel, the slope formula and show that both sides have the same slope.
Two sides (or diagonals) are perpendicular, the slope formula, and show that the slopes of the two sides (or diagonals) are negative reciprocals.
Diagonals bisect each other, the midpoint formula, and show that both diagonals have the same midpoint.
That an angle is a right angle, the slope formula, and show that the slopes of the two intersecting segments that create the angle are negative reciprocals.
a quadrilateral is a parallelogram, methods to show that both pairs of opposite sides are congruent OR both pairs of opposite sides parallel OR one pair of opposite sides are both congruent and parallel OR that the diagonals bisect each other
a quadrilateral is a rhombus, methods to first show the quadrilateral is a parallelogram, plus show it has one pair of consecutive sides congruent OR that its diagonals are perpendicular.
a quadrilateral is a rectangle, methods to first show the quadrilateral is a parallelogram, plus show it contains one right angle OR that its diagonals are congruent.
a quadrilateral is a square, methods to show the quadrilateral is a parallelogram, plus show its also a rhombus, plus show its also a rectangle.
a quadrilateral is a trapezoid, methods to show the quadrilateral has one pair of opposite sides parallel AND one pair of opposite sides non-parallel
a quadrilateral is an isosceles trapezoid, methods to first show its a trapezoid, plus show that the non-parallel sides are congruent OR that its diagonals are congruent.
Created by: mburke79