Question

G is 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

Answer 1

2,3,4,5 are the answers

Explanation:

Answer 2

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.