DE is a perpendicular bisector of overline FG and they intersect at point H. Which of the following statements must be true? Select the two correct answers. point) FG DE angle DHF simeq angle DRG; overline DH simeq EH; FH simeq overline GH; angle FDH simeq angle DGH

Question

DE is a perpendicular bisector of overline FG and they intersect at point H. Which of the following statements must be true? Select the two correct answers. point) FG DE angle DHF simeq angle DRG; overline DH simeq EH; FH simeq overline GH; angle FDH simeq angle DGH

Answer 1

The two correct statements are:

1) angle FDH simeq angle DGH: Since DE is the perpendicular bisector of FG and they intersect at point H, angle FDH and angle DGH would be vertical angles and therefore congruent.

2) FH simeq overline GH: As DE is the perpendicular bisector of FG, FH and GH would be congruent since they are opposite sides of an isosceles triangle.