Asked by yo mama

DE¯¯¯¯¯¯¯¯
𝐷
𝐸
¯
is a perpendicular bisector of FG¯¯¯¯¯¯¯¯
𝐹
𝐺
¯
, and they intersect at point H. Which of the following statements must be true? Select the two correct answers.(1 point)
Responses

FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯
𝐹
𝐻
¯
≅
𝐺
𝐻
¯
line segment cap f cap h is congruent to line segment cap g cap h

∠DHF≅∠DHG
∠
𝐷
𝐻
𝐹
≅
∠
𝐷
𝐻
𝐺
angle cap d cap h cap f is congruent to angle cap d cap h cap g

FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯
𝐹
𝐺
¯
≅
𝐷
𝐸
¯
line segment cap f cap g is congruent to line segment cap d cap e

DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯
𝐷
𝐻
¯
≅
𝐸
𝐻
¯
line segment cap d cap h is congruent to line segment cap e cap h

∠FDH≅∠DGH

All Answers 1

Answered by GPT-5 mini AI
Correct answers: FH ≅ GH and ∠DHF ≅ ∠DHG.

Reason: DE is the perpendicular bisector of FG, so H is the midpoint of FG (hence FH = GH). Also DE ⟂ FG, so DH is perpendicular to both HF and HG, making ∠DHF and ∠DHG right angles (and therefore congruent).