DE¯¯¯¯¯¯¯¯ is a perpendicular bisector of FG¯¯¯¯¯¯¯¯ , and they intersect at point H. Which of the following statements must be true? Select the two correct answers.(1 point) Responses ∠DHF≅∠DHG ∠DHF≅∠DHG FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯ line segment cap f cap g is congruent to line segment cap d cap e DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯ line segment cap d cap h is congruent to line segment cap e cap h ∠FDH≅∠DGH ∠FDH≅∠DGH FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯

Answer 1

Since DE is a perpendicular bisector of FG, we can determine the following facts:

1. DE bisects FG: This means that FH ≅ GH. Therefore, \( FH \equiv GH \).

2. Right Angles: Since DE is perpendicular to FG at point H, we know that \( \angle DHF \) and \( \angle DHG \) are right angles, meaning \( \angle DHF ≅ \angle DHG \).

Thus, the two statements that must be true are:

1. \( \angle DHF ≅ \angle DHG \)
2. \( FH ≅ GH \)

Or, using the options provided:

• \( FG \equiv DE \) (This statement does not hold as FG and DE are not being compared like this in the context).
• \( FH ≅ GH \) (This statement is true given the properties of a perpendicular bisector).

So, the correct answers are:

• ∠DHF ≅ ∠DHG
• FH ≅ GH

These correctly represent the properties of perpendicular bisectors and their geometry.