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Distance formula

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Slope

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Midpoint Formula

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Point slope formula of a line

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Equation of a line

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y = mx +b

m is slopeb is y-intercept

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Slope

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Parallel Lines

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Parallel lines have equal slopes

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Perpendicular Lines

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Perpendicular lines have opposite reciprocal slopes

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Equation of a Circle

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Where: Center: (h, k) and radius =

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Finding the equation of a circle given two endpoints of the diameter

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• Use midpoint to find the center• Use distance (between center and one endpoint) to find the radius• Plug into equation of a circle

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Find the equation of a perpendicular bisector

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1. Find slope 2. Flip and change the sign of the slope from step 1.3. Find the midpoint.4. Plug answers from step 2 and 3 into point slope

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Prove a parallelogram

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Find the midpoint of both diagonalsIf they match then…

It is a parallelogram because diagonals bisect

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Prove a Rectangle

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Use DISTANCE to find the length of all four sidesIf Both sets of opposite sides are = then…

It is a rectangle because both sets of opposite sides are congruent

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Prove a Rhombus

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Use DISTANCE to find the length of all four sidesIf ALL sides are = then…

It is a rhombus because all sides are congruent

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Prove a Square

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Use DISTANCE to find the length of all four sides and SLOPE of 2 adjacent sidesIf ALL sides are = and the slopes are opposite reciprocals then…

It is a square because all sides are congruent and adjacent sides are perpendicular

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Prove a Trapezoid

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Find the SLOPE of all four sidesIf two slopes are = and two are then…

It is a trapezoid because there is only one set of opposite parallel sides.

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Prove an isosceles trapezoid

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Find the SLOPE of all four sides and the DISTANCE of the non-parallel sidesIf two slopes are = and two are and the non-parallel sides are = then…

It is an isosceles trapezoid because there is only one set of opposite parallel sides and the legs are congruent.

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