Creating Right Triangles!
Creation of this resource was inspired by this Open Middle problem submitted by Erick Lee.
Using the digits 1-8 as coordinates of points A, B, and C at most one time each, position A, B, and C so they serve as vertices of a RIGHT TRIANGLE.
How many possibilities exist here?
1.
List 3 ordered pairs (with no repeated coordinate digits) that make a right triangle. Then with these coordinates, prove algebraically that this triangle is indeed a right triangle.
2.
List a different set of 3 ordered pairs (with no repeated coordinate digits) that make a right triangle. Then with these coordinates, prove algebraically that this triangle is indeed a right triangle.