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.
part a: identify a pair of similar triangles
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

answer:

  a) δdef ~ δged

  b) aa similarity: ∠d≅∠g; ∠e≅∠e

  c) ed = 4

step-by-step explanation:

a) all three of the right triangles in the figure are similar to each other. the ones relevant to the problem are δdef and δged.

__

b) any pair of right triangles in the figure shares at least one acute angle. that makes them similar by the aa similarity postulate. for triangles def and ged, the shared acute angle is angle e. the corresponding right angles are ∠d in δdef and ∠g in δged.

__

c) corresponding parts of similar triangles are proportional, so we can write

  ed/ef = eg/ed

"cross multiplying" gives

  ed² = ef·eg = 8·2 = 16

  ed = √16

  ed = 4

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right