Five-Minute Check (over Lesson 4-6) Main Ideas and Vocabulary California Standards Key Concept: Placing Figures on the Coordinate Plane Example 1: Position and Label a Triangle Example 2: Find the Missing Coordinates Example 3: Coordinate Proof Example 4: Real-World Example: Classify Triangles Lesson 7 Menu

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

Standard 17.0 Students prove theorems by using coordinate geometry, including the midpoint of a line segment, the distance formula, and various forms of equations of lines and circles. (Key) Lesson 7 CA

Lesson 7 KC1

Position and Label a Triangle Position and label right triangle XYZ with leg d units long on the coordinate plane. 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. 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: Animation: Placing Figures on the Coordinate Plane for Coordinate Proofs Lesson 7 Ex1

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? A B C D Lesson 7 CYP1

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

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, ?). The y-coordinate for S is the distance from R to S. Since ΔQRS is an isosceles right triangle, 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). Answer: Q(0, 0); S(c, c) Lesson 7 Ex2

Name the missing coordinates of isosceles right ΔABC. 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) A B C D Lesson 7 CYP2

Given: ΔXYZ is isosceles. 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. Given: ΔXYZ is isosceles. Prove: Lesson 7 Ex3

Proof: By the Midpoint Formula, the coordinates of W, 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, . Lesson 7 Ex3

Finish the following coordinate proof to prove that the segment drawn from the right angle to the midpoint of the hypotenuse of an isosceles right triangle is perpendicular to the hypotenuse. Lesson 7 CYP3

Proof: The coordinates of the midpoint D are The slope of is or 1. The slope of or –1, therefore because ____. ? A B C D A. their slopes are opposite. B. the sum of their slopes is zero. C. the product of their slopes is –1. D. the difference of their slopes is 2. Lesson 7 CYP3

Classify Triangles 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. Lesson 7 Ex4

or undefined. The slope of or 0, therefore ΔDEF is a right triangle. 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. Lesson 7 Ex4

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. Lesson 7 CYP4

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

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

End of Lesson 7