State whether each of the following can be determined with coordinate geometry.Yes, with the distance or midpoint formulas.Example XYZ has vertices X(1, 0), Y ( 2, 4 ), and Z ( 4, 4). To determine whether opposite sides are parallel, or whether diagonals or sides are perpendicular, use the Slope Formula. How will you place the rhombus in a coordinate plane What formulas will you need to use The altitude to the base of an isosceles triangle bisects the base. Coordinate geometry proofs require an understanding of the properties of shapes such as triangles, quadrilaterals, and other polygons. To determine the coordinate of the midpoint of a side, or whether the diagonals bisect each other, use the Midpoint Formula. Proof Think About a PlanIf a parallelogram is a rhombus, its diagonals are perpendicular (Theorem 6-13). State whether each of the following can be determined with coordinate geometry. Use coordinate geometry to prove each statement.Connecting Algebra to Proofs Algebra I Quiz - Quizizz File Name. What types of proofs can be done with C.G.? ĭeciding whether C.G. Proofs Using Coordinate Geometry 348 Chapter 6 Quadrilaterals What Youll Learn To. Therefore the diagonals of rectangles are congruent. How Does a Coordinate Proof Work? Proofs using coordinate geometry use the slope, midpoint, and distance formulas to proof rules and theorems.Įx: 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.
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