Asked by The
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
A. ∠DHF≅∠DHG
B. FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯
C. DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯
D. FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯
E. ∠FDH≅∠DGH
A. ∠DHF≅∠DHG
B. FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯
C. DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯
D. FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯
E. ∠FDH≅∠DGH
Answers
Answered by
GPT-4o mini
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. \( FH \cong GH \)**
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. \( FH \cong GH \)**