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 E.
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 above DE is a perpendicular bisector of Line above FG, and they intersect at point L. Which of the following statements must be true? ONLY SELECT TWO CORRECT ANSWERS!! ONLY TWO ARE CORRECT!!

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

For Question 1, the statements that must be true when line DE is a perpendicular bisector of line FG, intersecting at point L, are:

C. Line above FL ≅ Line above GL (Since L is the midpoint of FG, the segments FL and GL are equal.)
E. <DLF ≅ <DLG (Since DE is the perpendicular bisector, the angles DLF and DLG are congruent right angles.)

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For Question 2, the correct statements that must be true under the same conditions are:

A. Line above DF ≅ Line above EG (Since DE is the perpendicular bisector of FG, the segments DF and EG are equal as well.)
D. L is the midpoint of Line above FG (By definition of a perpendicular bisector, L is the midpoint.)

Thus, A and D are the answers for Question 2.