MATH SOLVE

5 months ago

Q:
# G is the incenter, or point of concurrency, of the angle bisectors of ΔACE.Which statements must be true regarding the diagram?BG ≅ AGDG ≅ FGDG ≅ BGGE bisects ∠DEFGA bisects ∠BAF

Accepted Solution

A:

BG ≅ AGBG 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 ≅ FGDG 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 ≅ BGAgain 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 ∠DEFAs said in the question GE is the angle bisector , So yes GE bisects ∠DEF.This Statement is true.

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

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

DG ≅ FGDG 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 ≅ BGAgain 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 ∠DEFAs said in the question GE is the angle bisector , So yes GE bisects ∠DEF.This Statement is true.

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

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