Geometry Lesson 4 – 8 Triangles and Coordinate Proof Objective: Position and label triangles for use in coordinate proofs. Write coordinate proofs.

Coordinate Proof Coordinate proof – use figures in the coordinate plane and algebra to prove geometric concepts.

Key Concept 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.

Position and label right triangle MNP on the coordinate plane so that leg MN is a units long and leg NP is b units long.

Position and label isosceles triangle JKL on the coordinate plane so that its base JL is a units long, vertex K is on the y-axis, and the height of the triangle is b units.

Identify Missing Coordinates of isosceles triangle XYZ Z (a, 0) X (0, 0)

Name the missing coordinates of isosceles right triangle ABC. B (0, 0) C (a, 0) A (0, a)

Write a coordinate proof to show that a line segment joining the midpoints of two sides of a triangle is parallel to the third side. Sketch a picture. Use numbers that will make the problem easier. Midpoint deals with dividing by 2 so use multiples of 2 to make it simple. Cont…

Proof Using Midpoint formula: Using Slope formula: Since the slopes are equal,

The Bermuda Triangle is a region formed by Miami, Florida, San Jose, Puerto Rico, and Bermuda. The approximate coordinates are given. Write a coordinate proof to prove the Bermuda triangle is scalene. Since all sides are different, Triangle MBP is scalene.

Homework Pg – 4 all, 8 – 18 E, 32, 38 – 46 E