Obj. 20 Coordinate Proof
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The student is able to prove conjectures about geometric figures on a coordinate plane using coordinate proofs. A coordinate proof uses coordinate geometry and algebra by placing a figure in the coordinate plane and using properties like slope, distances between points, and coordinates of vertices to prove statements about the figure. For example, a coordinate proof can show that the diagonals of a rectangle bisect each other by finding the midpoints of the diagonals have the same coordinates.
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Obj. 20 Coordinate Proof
- 1. Obj. 20 Coordinate Proof The student is able to (I can): • Prove conjectures about geometric figures on a coordinate plane
- 2. coordinate proof A style of proof that uses coordinate geometry and algebra. Once a figure is placed in the coordinate plane, we can use slope, the coordinates of the vertices, the Distance Formula, or the Midpoint Formula to prove statements about the figure. Example Given: Rectangle ABCD with A(0, 0), B(4, 0), C(4, 10), and D(0, 10) Prove: The diagonals bisect each other. The midpoint of AC is (2, 5), and the midpoint of BD is also (2, 5). Therefore, the two diagonals bisect each other.
- 3. Example Given: A(0, 0), B(7, 1), C(10, 5), and D(3, 4) Prove: ADB ≅ CBD 2 2 AB = ( 7 − 0 ) + ( 1 − 0 ) = 50 C D 2 2 2 CB = ( 10 − 7 ) + ( 5 − 1) = 5 2 B A 2 AD = ( 3 − 0 ) + ( 4 − 0 ) = 5 2 CD = ( 3 − 10 ) + ( 4 − 5 ) = 50 Therefore, AD ≅ CB and AB ≅ CD DB ≅ BD by Refl. prop. ≅ Therefore, ADB ≅ CBD by SSS