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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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