Question

1. Points B, D, and F are midpoints of the sides of △ACE. EC = 38 and DF = 16. Find AC. The diagram is not to scale.

2.
−−→
DF bisects ∠EDG. Find FG. The diagram is not to scale.
plz help 20 points

Answer 1

1) AC = 32

2) FG = 14

Explanation:

1) In Δ ACE

∵ D is the mid-point of EC

∵ F is the mid-point of AE

∴ FD // AC and FD = 1/2 AC

∵ FD = 16

∴ AC = 16 × 2 = 32

2) In the two triangles DEF and DGF

∵ m∠ DEF = m∠DGF = 90°

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

∵ DF is a common side

∴ The two 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