Gis the incenter, or point of concurrency, of the angle bisectors of δace.

which statements must be true regarding the diagram?

bg ≅ ag
dg ≅ fg
dg ≅ bg
ge bisects ∠def
ga bisects ∠baf

BG ≅ AG

BG is the perpendicular to the side of the triangle while AG is the angle bisector , So BG cannot equal AG , So BG cannot be congruent to AG. Hence first is false.

DG ≅ FG

DG And FG both are the perpendicular to the sides from the incentre of the circle , Hence DG and FG are congruent , So second statement is true.

DG ≅ BG

Again DG and BG both are the perpendicular to the sides from the incentre of the circle , Hence DG and BG are congruent , So third statement is true.

GE bisects ∠DEF

As said in the question GE is the angle bisector , So yes GE bisects ∠DEF.

This Statement is true.

GA bisects ∠BAF

Again As said in the question GA is the angle bisector , So yes GA bisects ∠BAF.

Hence 2nd, 3rd , 4th , and 5th options are correct.

volume of cube=(side×side×side)

=16×16×16

=4096in^3