Question
DE is a perpendicular bisector of FG, and they intersect at point L. Which of the following statements must be true? Select the
two correct answers. R points)
Line above DL ≅ EL
< DFL ≅ DGL
Line above FL ≅ GL
Line above FG ≅ DE
< DLF ≅ DLG
two correct answers. R points)
Line above DL ≅ EL
< DFL ≅ DGL
Line above FL ≅ GL
Line above FG ≅ DE
< DLF ≅ DLG
Answers
GPT-4o mini
To analyze the given information that line DE is a perpendicular bisector of line FG and intersects at point L, let's examine the statements one by one:
1. **Line DL ≅ EL**: This statement is true because DE is the perpendicular bisector of FG. By definition, a perpendicular bisector divides a segment into two equal parts. Therefore, DL is equal to EL.
2. **∠DFL ≅ ∠DGL**: This is also true. As DE is a perpendicular bisector, it creates two right angles (90 degrees) at point L. Since DL = EL and they are both radii to the same angle, these angles are congruent.
3. **Line FL ≅ GL**: This statement is not necessarily true unless we know more about how FL and GL relate to the triangle formed by points D, F, and G.
4. **Line FG ≅ DE**: This statement is false. FG and DE are not comparable in terms of length unless otherwise stated.
5. **∠DLF ≅ ∠DLG**: This statement is true because angle DLF and angle DLG share a common side (DL) and are opposite angles formed by the intersecting lines. This makes them congruent.
Based on the explanations above, the two correct answers are:
- **Line DL ≅ EL**
- **∠DFL ≅ ∠DGL**
You can choose these two statements.
1. **Line DL ≅ EL**: This statement is true because DE is the perpendicular bisector of FG. By definition, a perpendicular bisector divides a segment into two equal parts. Therefore, DL is equal to EL.
2. **∠DFL ≅ ∠DGL**: This is also true. As DE is a perpendicular bisector, it creates two right angles (90 degrees) at point L. Since DL = EL and they are both radii to the same angle, these angles are congruent.
3. **Line FL ≅ GL**: This statement is not necessarily true unless we know more about how FL and GL relate to the triangle formed by points D, F, and G.
4. **Line FG ≅ DE**: This statement is false. FG and DE are not comparable in terms of length unless otherwise stated.
5. **∠DLF ≅ ∠DLG**: This statement is true because angle DLF and angle DLG share a common side (DL) and are opposite angles formed by the intersecting lines. This makes them congruent.
Based on the explanations above, the two correct answers are:
- **Line DL ≅ EL**
- **∠DFL ≅ ∠DGL**
You can choose these two statements.