1. Triangles and Coordinate Proof
LESSON 4–8
Triangles and Coordinate Proof

2. You used coordinate geometry to prove triangle congruence.
Position and label triangles for use in coordinate proofs.
Write coordinate proofs.
Then/Now

3. Use the origin as vertex X of the triangle.
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.
Example 1

4. 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:
Example 1

5. Concept

6. Name the missing coordinates of isosceles right triangle QRS.
Identify Missing Coordinates
Name the missing coordinates of isosceles right triangle QRS.
Example 2

7. 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)
Example 2

8. Given: ΔXYZ is isosceles.
Write a 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.
Given: ΔXYZ is isosceles.
Prove:
Example 3

9. 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.
Example 3

10. FLAGS Tracy wants to 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.
Example 4