DE is a perpendicular bisector of FG, and they intersect at point L. Which of the following statements must be true? Select the

Question

two correct answers. R points)

Line above DL ≅ EL
< DFL ≅ DGL
Line above FL ≅ GL
Line above FG ≅ DE
< DLF ≅ DLG

Answer 1

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.