1. Section 4.8 Notes: Triangles and Coordinate Proof
EQ: How can you use a coordinate plane to write a proof?

2. How to place figures correctly on the coordinate plane.
Coordinate Proofs
Using figures in the coordinate plane and algebra to prove geometric concepts
How to place figures correctly on the coordinate plane.
Step 1: Use the origin as the vertex or center of the triangle
Step 2: Place at least one side of a triangle on an axis
Step 3: Keep the triangle within the first quadrant if possible
Step 4: Use the coordinates to make the computations as simple as possible.

3. Example 2:
Name the missing coordinates of isosceles right triangle QRS.
Q(0, 0)
Since the triangle is an isosceles right triangle, 𝑄𝑅 ≅ 𝑆𝑅 and since the length of 𝑄𝑅 is c, the length of 𝑆𝑅 is also c.
Therefore S(c, c)

4. Example 4: Name the missing coordinates of each triangle.
The point C divides the base in half so if the length of 𝐴𝐵 is 2p then the x coordinate of C is 2p/2 which is p.
Therefore C (p, q)

5. You Try!
Name the missing coordinates of each triangle.
T(2a, 2a)

6. You Try! Name the missing coordinates of each triangle. F(0, b)
E(-2g, 0)