7. DF bisects EDG. Find FG. The diagram is not to scale. ​

THIS USER ASKED 👇

7. DF bisects EDG. Find FG. The diagram is not to scale. ​

THIS IS THE BEST ANSWER 👇

1) AC = 32

2) FG = 14

Step by step explanation:

1) In Δ ACE

DD is the center of CE

∵ F is the midpoint of AE

∴ FD // AC and FD = 1/2 AC

∵ FD = 16

∴ AC = 16 × 2 = 32

2) In both triangles DEF and DGF

∵ m∠ DEF = m∠DGF = 90 °

∵ m∠EDF = m∠GDF ⇒ DF EDG angle divider

∵ DF is a common side

∴ Both triangles are congruent

∴ EF = GF

∵ EF = n + 9

∵ GF = 4n – 6

∴ 4n – 6 = n + 9 ⇒ 4n – n = 9 + 6

∴ 3n = 15 ⇒ ∴ n = 15 ÷ 3

∴ n = 5

∴ FG = 4 (5) – 6 = 20 – 6 = 14