Question

if ∠dfe ≅ ∠dfg and de = 65, what is dg? dg =

Explanation:

Step1: Recall angle - bisector theorem

The ray DF is the angle - bisector of ∠EFG (since ∠DFE≅∠DFG), and DG⊥FG, DE⊥FE. According to the angle - bisector theorem, the distance from a point on an angle - bisector to the two sides of the angle is equal.

Step2: Apply the theorem

Since DF is the angle - bisector of ∠EFG and DG and DE are the distances from point D to the sides of the angle, we have DG = DE.

Answer:

65