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**Proofs Using Coordinate Geometry**

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**How Does a Coordinate Proof Work?**

Proofs using coordinate geometry use the slope, midpoint, and distance formulas to proof rules and theorems.

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**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.

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**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.

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**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

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**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.

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

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