1. Lesson 7 Menu 1.Name two congruent segments if  1   2 2.Name two congruent angles if RS  RT. 3.Find m  R if m  RUV = 65. 4.Find m  C if ΔABC is isosceles with AB  AC and m  A = 70. 5.Find x if ΔLMN is equilateral with LM = 2x – 4, MN = x + 6, and LN = 3x – 14.

2. Lesson 7 MI/Vocab coordinate proof Position and label triangles for use in coordinate proofs. Write coordinate proofs.

3. Lesson 7 KC1

4. Lesson 7 Ex1 Position and Label a Triangle Use the origin as vertex X of the triangle. Place the base of the triangle along the positive x-axis. Position the triangle in the first quadrant. Since Z is on the x-axis, its y-coordinate is 0. Its x-coordinate is d because the base is d units long. Position and label right triangle XYZ with leg d units long on the coordinate plane.

5. Lesson 7 Ex1 Position and Label a Triangle Since triangle XYZ is a right triangle the x-coordinate of Y is 0. We cannot determine the y-coordinate so call it b. Answer:

6. A.A B.B C.C D.D Lesson 7 CYP1 Which picture on the following slide would be the best way to position and label equilateral triangle ABC with side w units long on the coordinate plane?

7. A.A B.B C.C D.D Lesson 7 CYP1 A.B. C.D.

8. Lesson 7 Ex2 Find the Missing Coordinates Name the missing coordinates of isosceles right triangle QRS. Q is on the origin, so its coordinates are (0, 0). The x-coordinate of S is the same as the x-coordinate for R, (c, ?). Answer: Q(0, 0); S(c, c) The distance from Q to R is c units. The distance from R to S must be the same. So, the coordinates of S are (c, c). The y-coordinate for S is the distance from R to S. Since ΔQRS is an isosceles right triangle,

9. Lesson 7 CYP2 1.A 2.B 3.C 4.D A.A(d, 0); C(0, 0) B.A(0, f); C(0, 0) C.A(0, d); C(0, 0) D.A(0, 0); C(0, d) Name the missing coordinates of isosceles right ΔABC.

10. Lesson 7 Ex3 Coordinate Proof Write a coordinate proof to prove that the segment that joins the vertex angle of an isosceles triangle to the midpoint of its base is perpendicular to the base. The first step is to position and label an isosceles triangle on the coordinate plane. Place the base of the isosceles triangle along the x-axis. Draw a line segment from the vertex of the triangle to its base. Label the origin and label the coordinates, using multiples of 2 since the Midpoint Formula takes half the sum of the coordinates. Prove: Given: ΔXYZ is isosceles.

11. Lesson 7 Ex3 Coordinate Proof Proof: By the Midpoint Formula, the coordinates of W, the midpoint of, is The slope of or undefined. The slope of is therefore,.

12. Lesson 7 Ex4 DRAFTING Write a coordinate proof to prove that the outside of this drafter’s tool is shaped like a right triangle. The length of one side is 10 inches and the length of another side is 5.75 inches. Classify Triangles

13. Lesson 7 Ex4 Classify Triangles Proof: The slope of or undefined. The slope of or 0, therefore ΔDEF is a right triangle. The drafter’s tool is shaped like a right triangle.

14. Lesson 7 CYP4 FLAGS Write a coordinate proof to prove this flag is shaped like an isosceles triangle. The altitude is 16 inches and the base is 10 inches.

15. A.A B.B C.C D.D Lesson 7 CYP4 A.(10, 10) B.(10, 5) C.(16, 10) D.(16, 5) What is the ordered pair for Point C?

16. A.A B.B C.C D.D Lesson 7 CYP4 Next, determine the lengths of CA and CB. What are the lengths of both of these? A.21 B.16 C. D.10