5 6 Coordinate Proofs Geogebra Warmup 1 2

5. 6 Coordinate Proofs

Geogebra Warm-up 1) 2) 3) 4) 5) Turn on axes and gridlines. Draw a segment A(0, 0) B(6, 0). Construct a line x=3. Put a point E on that line (x=3). Prove Triangle AEC is congruent to Triangle BEC without using the angle or length measuring tool. (Don’t delete, we will continue with this file)

(cont. ) 6) Change the coordinates of E to the point (3, 3). 7) Prove AEB is an isosceles right triangle.

Coordinate Proof Proving conjectures about figures in the coordinate plane. You can use variables in your coordinates to prove conjectures about all figures of a certain type. The following are used heavily in coordinate proofs: -Distance Formula -Midpoint Formula -Pythagorean Thm -CPCTC -SSS -Slopes

Guided Practice • Place each figure on a coordinate plane in a way that is convenient for finding side lengths and assign coordinates (using variable or constants) to each vertex. – Rectangle – Scalene Triangle – Isoscles Right Triangle – Square – Circle

Given: Coordinates in picture Prove: y axis bisects angle ABC

Prove segment BD bisects angle ABC.

• Given a triangle with coordinates O(0, 0) B(a, 0) J(a, b), find if it is a right triangle and find the length of each side.