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

Question

A. ∠DHF≅∠DHG
B. FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯
C. DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯
D. FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯
E. ∠FDH≅∠DGH

Answer 1

Given that \( DE \) is the perpendicular bisector of \( FG \) and they intersect at point \( H \), we can analyze the provided statements.

1. Since \( DE \) is the perpendicular bisector of \( FG \):

   • This means that \( H \) is the midpoint of \( FG \).
   • Thus, \( FH \cong GH \) (i.e., \( FH = GH \)).
   • Therefore, statement D \( ( FH \cong GH ) \) is true.

2. Additionally, because \( DE \) is a perpendicular bisector, it intersects \( FG \) creating two right angles at point \( H \):

   • This results in \( \angle DHF \cong \angle DHG \) (since they are both right angles).
   • Therefore, statement A \( ( \angle DHF \cong \angle DHG ) \) is also true.

The two correct answers are:

• A. \( \angle DHF \cong \angle DHG \)
• D. \( FH \cong GH \)