Seth is using the figure shown below to prove the pythagorean theorem using triangle similarity:

in the given triangle def, angle d is 90° and segment dg is perpendicular to segment ef.

the figure shows triangle def with right angle at d and segment dg. point g is on side ef.

part a: there are three similar angles i'm using dgf and def

part b: explain how you know the triangles from part a are similar.

part c: if eg = 2 and ef = 8, find the length of segment ed. show your work.