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Proofs Using Coordinate Geometry

Proofs Using Coordinate Geometry. How Does a Coordinate Proof Work?. Proofs using coordinate geometry use the slope, midpoint, and distance formulas to proof rules and theorems. Ex: Prove a Rectangle H as C ongruent D iagonals.

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Proofs Using Coordinate Geometry

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  1. Proofs Using Coordinate Geometry

  2. How Does a Coordinate Proof Work? Proofs using coordinate geometry use the slope, midpoint, and distance formulas to proof rules and theorems.

  3. Ex: Prove a Rectangle Has Congruent Diagonals Step 1: Place the figure on the xy-axis Step 2: Correctly label the points Step 3: Write a Given and Prove statement Step 4: Use slope, mp, or distance formulas Step 5: Write a concluding statement ( 0, b ) ( a , b ) B C D A ( 0 , 0 ) ( a , 0 ) Given: ABCD is a rectangle Prove: Diagonals are = (AC=BD) AC and BD have the same length. Therefore the diagonals of rectangles are congruent.

  4. What types of proofs can be done with C.G.? • The slope formula can show: • Segments are parallel. • Segments are perpendicular. • A figure has right angles. • The distance formula can show: • Segments have the same length • Two segments bisect each other • The midpoint formula can show: • The location of a midpoint • Two segments bisect each other.

  5. Deciding whether C.G. will work on a Proof. • State whether each of the following can be determined with coordinate geometry. • EF=GH • Yes, with the distance formula • BD ll AC • Yes, with the slope formula • <A=<B • No, unless both are right angles • FG bisects JG • Yes, with the distance or midpoint formulas

  6. Deciding whether C.G. will work on a Proof. • State whether each of the following can be determined with coordinate geometry. • Triangle LMN is isosceles • Yes, with the distance formula • The diagonals of Kite QRST are perpendicular • Yes, with the slope formula • <C and <D are supplementary • No.

  7. Homework P 335 (12-24) Worksheet - Proofs Using the Coordinate Plane

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