Geometry

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Author:
duhhitsjessie
ID:
22395
Filename:
Geometry
Updated:
2010-06-06 22:59:22
Tags:
Coordinate Geometry Proofs
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Description:
Coordinate Geometry
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  1. How to prove a quadrilateral a parallelogram.
    • 1. Prove both pairs of opposite sides congruent. [distance formula 4x]
    • 2. Prove both pairs of opposite sides are parallel [slope formula 4x]
    • 3. Prove one pair of opposite sides are both parallel and congruent [distance formua 2x, slope formula 2x]
    • 4. Prove diagonals bisect each other. If both diagonals have the same midpoint, they bisect eachother. [midpoint formula 2x]
  2. How to prove a quadrilateral is a rectangle.
    • FIRST: Prove the quadrilateral is a parallelogram.
    • THEN:
    • 1. Prove the diagonals are congruent [distance formula 2x]
    • 2. Prove there is a right angle. [slope formula 2x, show that two adjacent sides have negative reciprocal slopes]
  3. How to prove a quadrilateral is a rhombus.
    • 1. Prove all sides are congruent. [distance formula 4x- easiest way]
    • *doing this proves it is a parallelogram & a rhombus at the same time
    • 2. Prove it is a parallelogram with a pair of adjacent sides congruent [distance formula]
    • 3. Prove it is a parallelogram with diagonals perpendicular to eachother [slope formula]
  4. How to prove a quadrilateral is a square.
    • 1. Prove it is a rectangle with a pair of adjacent sides congruent. [distance formua 4x]
    • *to prove it is a rectangle, you have to prove it is a parallelogram first*
    • 2. Prove it is a rectangle with the diagonals perpendicular to eachother. [slope formula 2x]
    • 3. Prove it is a rectangle with a pair of adjacent sides that are perpindicular [slope formula 2x]
  5. How to prove a quadrilateral is a trapezoid.
    • 1. Prove that one pair of opposite sides are parallel. [slope formua 2 times]
    • AND
    • 2. Prove that one pair of opposite sides are NOT parallel. [slope formula 2x]

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