Answer:
ED = 4
Step-by-step explanation:
A & B) Triangles FGD and DGE are similar. Set <DFG to x. We can say that m<DGF, m<DGE, and m<EDF are 90 because they are right. Using triangle angle sum theorem in triangle DEF, we can say that m<DEG = 90 - x. And we can use it again to say in triangle FGD to say m<FDG is also 90-x. From AA we can say the triangles FGD and DGE are congruent.
C) In addition to the two triangles above, triangle FDE would also be congruent due to AA. We can write the following equations using the properties of similar triangles:
DGE FDE
EG = ED*y --> 2 = ED*y
ED * 1/y = EF --> ED * 1/y = 8 --> ED = 8y
We can substitute:
2 = 8y^2
1/4 = y^2
y = 1/2
This means ED = 8y = 8(1/2) = 4 --> ED = 4
