DE is a perpendicular bisector of FG, and they intersect at point L. Which of the following statements must be true? Select the two correct answers.

Question

a. FG ≅ DE
b. ∠DLF ≅ ∠DLG
c. DL ≅ EL
d. ∠DFL ≅ ∠DGL
e. FL ≅ GL

Answer 1

Since DE is the perpendicular bisector of FG and they intersect at point L, we can deduce the following:

1. DE being a bisector means that it divides FG into two equal segments. Therefore, FL ≅ GL.
2. DE being perpendicular to FG means that it creates right angles at the intersection point, thus ∠DLF ≅ ∠DGL (both are right angles).

From these observations, the two statements that must be true are:

d. ∠DFL ≅ ∠DGL
e. FL ≅ GL

So the correct answers are (d) and (e).