Question
Question 1
Line above DE is a perpendicular bisector of Line above FG, and they intersect at point L. Which of the following statements must be true? Select the two correct answers.
The correct answers are C. And D.
A. Line above DL ≅ Line above EL
B. <DFL ≅ <DGL
C. Line above FL ≅ Line above GL
D. Line Above FG ≅Line above DE
E. <DLF ≅ <DLG
Question 2
Line Line above DE is a perpendicular bisector of Line above FG, and they intersect at point L. Which of the following statements must be true? Select the two correct answers.
A. Line above DF ≅ Line above EG
B. <DGL = 90°
C. <L is equidistant from points F and G
D. L is the midpoint of Line above FG
E. Line above DE || Line Above FG
Line above DE is a perpendicular bisector of Line above FG, and they intersect at point L. Which of the following statements must be true? Select the two correct answers.
The correct answers are C. And D.
A. Line above DL ≅ Line above EL
B. <DFL ≅ <DGL
C. Line above FL ≅ Line above GL
D. Line Above FG ≅Line above DE
E. <DLF ≅ <DLG
Question 2
Line Line above DE is a perpendicular bisector of Line above FG, and they intersect at point L. Which of the following statements must be true? Select the two correct answers.
A. Line above DF ≅ Line above EG
B. <DGL = 90°
C. <L is equidistant from points F and G
D. L is the midpoint of Line above FG
E. Line above DE || Line Above FG
Answers
GPT-4o mini
For both questions, let's analyze the statements based on the properties of a perpendicular bisector.
### Question 1 Analysis:
Given that line DE is a perpendicular bisector of line FG and intersects at point L:
A. Line DL ≅ Line EL
**(False)** - This statement is incorrect because while DE is a bisector, it only guarantees that DL = EL.
B. ∠DFL ≅ ∠DGL
**(False)** - This does not have to be true; angles ∠DFL and ∠DGL are not necessarily equal.
C. Line FL ≅ Line GL
**(True)** - As DE bisects FG, segments FL and GL are equal.
D. Line FG ≅ Line DE
**(False)** - There is no information given that FG and DE are equal as lengths; they are just intersecting.
E. ∠DLF ≅ ∠DLG
**(True)** - Since DE is a perpendicular bisector, the angles created at L by the line DE and line FG will be congruent.
### Correct Answers for Question 1:
C and E.
---
### Question 2 Analysis:
Since line DE is a perpendicular bisector of line FG and they intersect at point L:
A. Line DF ≅ Line EG
**(False)** - This does not have to be true based on the information provided.
B. ∠DGL = 90°
**(True)** - By definition of perpendicularity, DE forms a right angle at point L with FG.
C. Point L is equidistant from points F and G
**(True)** - This is true as point L is the point of intersection of the perpendicular bisector.
D. L is the midpoint of line FG
**(True)** - Since DE is a perpendicular bisector, it implies that L is the midpoint of FG.
E. Line DE || Line FG
**(False)** - DE is perpendicular to FG, not parallel.
### Correct Answers for Question 2:
C and D.
In summary:
- For Question 1, the correct answers are C and E.
- For Question 2, the correct answers are C and D.
### Question 1 Analysis:
Given that line DE is a perpendicular bisector of line FG and intersects at point L:
A. Line DL ≅ Line EL
**(False)** - This statement is incorrect because while DE is a bisector, it only guarantees that DL = EL.
B. ∠DFL ≅ ∠DGL
**(False)** - This does not have to be true; angles ∠DFL and ∠DGL are not necessarily equal.
C. Line FL ≅ Line GL
**(True)** - As DE bisects FG, segments FL and GL are equal.
D. Line FG ≅ Line DE
**(False)** - There is no information given that FG and DE are equal as lengths; they are just intersecting.
E. ∠DLF ≅ ∠DLG
**(True)** - Since DE is a perpendicular bisector, the angles created at L by the line DE and line FG will be congruent.
### Correct Answers for Question 1:
C and E.
---
### Question 2 Analysis:
Since line DE is a perpendicular bisector of line FG and they intersect at point L:
A. Line DF ≅ Line EG
**(False)** - This does not have to be true based on the information provided.
B. ∠DGL = 90°
**(True)** - By definition of perpendicularity, DE forms a right angle at point L with FG.
C. Point L is equidistant from points F and G
**(True)** - This is true as point L is the point of intersection of the perpendicular bisector.
D. L is the midpoint of line FG
**(True)** - Since DE is a perpendicular bisector, it implies that L is the midpoint of FG.
E. Line DE || Line FG
**(False)** - DE is perpendicular to FG, not parallel.
### Correct Answers for Question 2:
C and D.
In summary:
- For Question 1, the correct answers are C and E.
- For Question 2, the correct answers are C and D.