GH­­Lesson 4­8_notes.notebook October 23, 2015

4.8 Triangles and Coordinate Proof

Students will be able to . . .

• position and label triangles for use in coordinate proofs.

• write coordinate proofs.

Coordinate Proof

Proof that use figures in the coordinate plane and algebra to prove geometric concepts.

The coordinates are not always numeric. The coordinates may include variables.

Geometric Concept (isosceles triangles)

The altitude of an isosceles triangle from the vertex angle will bisect the base.

G H

F

L

GH­­Lesson 4­8_notes.notebook October 23, 2015

8

7 b

a

( , ) ( , )

( , )( , )

Placing Triangles on Coordinate Plane

1. Use the origin as a vertex or center of the triangle.

2. Place at least one side of a triangle on an axis.

3. Keep the triangle within the first quadrant if possible.

4. Use coordinates that make computations as simple as possible.

GH­­Lesson 4­8_notes.notebook October 23, 2015

Name the missing coordinates of isosceles right triangle QRS.

What are the characteristics of an isosceles right triangle?

GH­­Lesson 4­8_notes.notebook October 23, 2015

Example

(a) Find the midpoint of NM and label it Q.

(c) Find the lengths of MP and QR.

(b) Find the midpoint of NP and label it R.

(d) Write a coordinate proof to prove MP QR.

GH­­Lesson 4­8_notes.notebook October 23, 2015

GH­­Lesson 4­8_notes.notebook October 23, 2015