Question

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

Answer 1

Since Line DE is defined as the perpendicular bisector of Line FG and they intersect at point L, we can derive the following conclusions:

1. **Option A: Line DF ≅ Line EG.**
True. Since DE is the perpendicular bisector of FG, it means that point L is the midpoint of FG, making DF equal to EG.

2. **Option B: ∠DGL = 90°.**
True. By the definition of a perpendicular bisector, the angle formed between DE and FG at point L will be 90 degrees.

3. **Option C: Point L is equidistant from points F and G.**
True. Since L is the midpoint of FG and DE is the perpendicular bisector, the distances from L to F and L to G are equal.

4. **Option D: L is the midpoint of Line FG.**
True. By definition, a perpendicular bisector intersects the line segment at its midpoint.

5. **Option E: Line DE || Line FG.**
False. Line DE is perpendicular to Line FG, not parallel.

Therefore, the two statements that must be true are **A. Line DF ≅ Line EG** and **B. ∠DGL = 90°**.