Question

-HELP ASAP-

In the diagram below, DE is the perpendicular bisector of FG. Which of the following statements must be true?

Answer 1

C, a, d, and e just took the test

Answer 2

Options A, C, D and E are correct choices.

Explanation:

We have been given that DE is the perpendicular bisector of FG. We are asked to choose the correct options about our given statement.

Let us check our given choices one by one.

A.
`\overline{FH}\cong\overline{GH}`

We can see that at point H line DE bisects line FG, so by the definition of bisect line segment FH is congruent to line segment GH. Therefore, option A is the correct choice.

B.
`\overline{DH}\cong\overline{EH}`

Since we have not been given that FG also bisects DE, therefore option B is not a correct choice.

C. Line DE is perpendicular to line segment FG.

Since we have been given that line DE is perpendicular to line segment FG, therefore, option C is the correct choice.

D. H is the midpoint of FG.

Since we know that bisects means divides into two equal parts, therefore, point H is the midpoint of FG and option D is the correct choice.

E.
`\angle DHF` is a right angle.

Since perpendicular means that a line meets another line at 90 degrees, therefore, option E is the correct choice.

F. FG bisects line DE.

Since we have not been given that FG also bisects DE, therefore option F is not a correct choice.