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 )BCDA( 0 , 0 )( a , 0 )Given: ABCD is a rectangleProve: 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 lengthTwo segments bisect each otherThe midpoint formula can show:The location of a midpointTwo 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=GHYes, with the distance formulaBD ll ACYes, with the slope formula<A=<BNo, unless both are right anglesFG bisects JGYes, 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 isoscelesYes, with the distance formulaThe diagonals of Kite QRST are perpendicularYes, with the slope formula<C and <D are supplementaryNo.
7 HomeworkP 335 (12-24)Worksheet - Proofs Using the Coordinate Plane