1. 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

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

3. reminder
Distance Formula
Midpoint Formula
Slope Formula

4. 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

5. 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

6. 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.

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

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

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