Lesson 4.7 Objective: To learn how to prove triangles are congruent and general statements using Coordinate Proofs.

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Presentation transcript:

Lesson 4.7 Objective: To learn how to prove triangles are congruent and general statements using Coordinate Proofs

Coordinate Proof Proofs that use the coordinate plane, postulates, theorems, and definitions, and the Distance and Midpoint Formulas to prove general statements about figures.

Find the coordiantes place one of the vertices at the origin, then line up a side with either the x-axis or the y-axis. x y (0, 5) B C (8, 5) A D (0, 0) (8, 0)

example Place a right triangle that has legs of 6 units and 8 units in a coordinate plane. Give the coordinates of its vertices. Find the length of the hypotenuse x y B (0, 6) A C (8, 0) (0, 0) 10

Find the Coordinates P (h, y) (h, k) (x, y) Find the coordinates of P. M (0, k) P P (h, y) (h, k) (x, y) O (0, 0) N (h, 0)

example J (x, c) (x, y) (a + b, c) a b Find the coordinates of J. L (b, c) J a b J (x, c) (x, y) (a + b, c) O (0, 0) H (a, 0)

example Q Prove: (h, k + n) x y P (0, n) R (h, k) O (0, 0)

Summary Explain the process of a coordinate proof. Why is it important to carefully place a figure on the coordinate plane?