Question
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 DH¯¯¯¯¯¯¯¯¯≅EH¯¯¯¯¯¯¯¯ line segment cap d cap h is congruent to line segment cap e cap h FG¯¯¯¯¯¯¯¯≅DE¯¯¯¯¯¯¯¯ line segment cap f cap g is congruent to line segment cap d cap e ∠DHF≅∠DHG ∠DHF≅∠DHG FH¯¯¯¯¯¯¯¯≅GH¯¯¯¯¯¯¯¯ line segment cap f cap h is congruent to line segment cap g cap h ∠FDH≅∠DGH ∠FDH≅∠DGH
Answers
Answered by
GPT-4o mini
To analyze the given problem, we know that line segment DE is a perpendicular bisector of line segment FG, and they intersect at point H. With this information, we can determine which statements must be true.
1. **DH ≅ EH**: This statement is true because DE is a bisector, meaning it divides FG into two equal parts at H. Therefore, DH and EH must be congruent.
2. **FH ≅ GH**: This statement is also true because DE being the perpendicular bisector means it divides FG into two equal segments. Hence, FH and GH must be congruent.
The other options involve angle congruence which arises from DE being perpendicular to FG, but out of the choices provided, the most directly supported statements are:
- DH ≅ EH
- FH ≅ GH
These two statements must be true given the properties of perpendicular bisectors.
1. **DH ≅ EH**: This statement is true because DE is a bisector, meaning it divides FG into two equal parts at H. Therefore, DH and EH must be congruent.
2. **FH ≅ GH**: This statement is also true because DE being the perpendicular bisector means it divides FG into two equal segments. Hence, FH and GH must be congruent.
The other options involve angle congruence which arises from DE being perpendicular to FG, but out of the choices provided, the most directly supported statements are:
- DH ≅ EH
- FH ≅ GH
These two statements must be true given the properties of perpendicular bisectors.