**Geometry Chapter 4.7 Triangles and Coordinate Proof**

**A coordinate proof involves placing geometric figures in a coordinate plane. Then you will use**:

**1) Distance Formula**- to show segments are congruent

**2) Midpoint formula**- to show that the segment is bisected

**3) Slope formula**-

a) if 2 lines have the same slope, then the lines are parallel

b) if 2 lines have slopes that are negative reciprocals of each other, then the lines are perpendicular

**Example:**To show that ΔABC is an isosceles right triangle given A(0,0), B(0,6) and C(6,0).

1. slope of AB = (0-6)/(0-0) = undefined

2. slope of BC = (6 - 0)/(0 - 6) = 6/(-6) = -1

3. slope of AC = (0 - 0)/(0 - 6) = 0 / 6 = 0

Therefore AB is perpendicular to AC because horizontal and vertical lines are perpendicular to each other. therefore angle A is a right angle because perpendicular lines form right angles.

4. AB = 6, AC = 6, and BC = 6√2

so we can conclude that AB = AC because they have the same measure.

Therefore since ΔABC has one right angle and 2 congruent sides, it is an isosceles right triangle.