If you divide a 4 inch by 8 inch rectangle from corner to corner, what new shapes would you get? are they congruent? why or why not?

You get 2 congruent right triangles when you divide a rectangle diagonally.

(This is one way to show that the area of each of those triangles is 1/2*base*height. Rectangle area = (4in) (8 in) = 32 in2. Triangle area = (1/2) (4in) (8in) = 16 in2.