Unit 5 Lesson 4.7 Triangles and Coordinate Proofs

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Unit 5 Lesson 4.7 Triangles and Coordinate Proofs State Standards Lesson Goals 2: Write geometric proofs. 5: Prove triangles are congruent. 17: Prove theorems by using coordinate geometry. Place geometric figures in a coordinate plane and use the Distance and/or Midpoint formula to measure distances or locate points. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

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

reminder Distance Formula Midpoint Formula Slope Formula

Coordinate Proofs Draw a figure with one vertex at the origin, (0, 0). If possible, draw the sides along the x- and/or y-axis. x y

example Place a right triangle that has legs of 6 units and 8 units on a coordinate plane. Give the coordinates of its vertices. Find the length of the hypotenuse 10

example Place a rectangle with length 4 units and width 7 units in a coordinate plane. Give the coordinates of its vertices, Find the length of the diagonal.

example In the diagram, . Find the coordinates of B. x y

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

Today’s Assignment Give ALL answers in simplified radical form.