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Topic 9

Coordinate Geometry & Review

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Distance Formula

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Formula used to find the distance between two points on a graph.

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Midpoint Formula

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The point exactly in the middle of a segment.

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Slope Formula

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Slope is the change in y divided by the change in x (rise over run) of a line on a graph.

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Pythagorean Theorem

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If a triangle is a Right Triangle, then you can use the Pythagorean Theorem to help solve for a missing side length.

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Properties of a Parallelogram

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  • Opposite sides are congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary (= 180°).
  • The diagonals bisect each other.

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Properties of a Rectangle

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  • A rectangle is a Parallelogram.
  • Each interior angle is 90 degrees.
  • Diagonals are congruent.

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Properties of a Rhombus

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  • A Rhombus is a Parallelogram.
  • All sides are congruent.
  • Diagonals are perpendicular.
  • Diagonals bisect the angles of a rhombus.

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Properties of a Square

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  • A squares is a parallelogram.
  • A square is a rhombus.
  • A square is a rectangle.

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Properties of a Trapezoid

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A quadrilateral with ONE pair of parallel sides (bases).

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Isosceles Trapezoid

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  • Non parallel sides are congruent.
  • Lower base angles are congruent.
  • Upper base angles are congruent.
  • Any lower base angle is supplementary to any upper base angle.
  • The diagonals are congruent.

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Properties of a Kite

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  • Two pairs of consecutive, congruent sides
  • Congruent non-vertex angles
  • Diagonals are perpendicular.

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Equation of a Circle

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Circumcenter

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The point of concurrency (intersection) of the perpendicular bisectors of a triangle.

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Incenter

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The point of concurrency (intersection) of the angle bisectors of a triangle.

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Centroid

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The point of concurrency (intersection) of the three medians of a triangle.

-Center of Gravity

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Orthocenter

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The point of concurrency (intersection) of the three altitudes of a triangle.

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