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: identify a pair of similar triangles. (2 points)

part b: explain how you know the triangles from part a are similar. (4 points)

part c: if eg = 2 and ef = 8, find the length of segment ed. show your work. (4 points)

Problems and applications q5 four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. here is their willingness to pay for each film: willingness to pay (dollars) shen antonio dmitri jake first film 10 9 8 3 second film 8 7 6 2 third film 6 5 4 1 fourth film 4 3 2 0 fifth film 2 1 0 0 within the dorm room, the showing of a movie a public good. if it costs $12 to rent a movie, the roommates should rent movies in order to maximize the total surplus. suppose the roommates choose to rent the optimal number of movies you just indicated and then split the cost of renting equally. this means that each roommate will pay $ .