Question

dh is a perpendicular bisector of fg, and they intersect at point h. which of the following statements must be true? select the two correct answers (1 point)∠dhp ≅ ∠dhg
fg ≅ de
fh ≅ gh
∠fdh ≅ ∠dgh
dh ≅ eh

Explanation:

Step1: Recall the definition of a perpendicular bisector

A perpendicular bisector of a segment divides the segment into two equal - length segments and is perpendicular to the segment. If \(DH\) is the perpendicular bisector of \(FG\), then by the definition of a perpendicular bisector, \(\overline{FG}\cong\overline{DE}\) (assuming some relation in the geometric figure where the bisector property is applied in terms of congruent segments related to the bisected segment) and \(\angle DHF\cong\angle DHG\) (since the perpendicular bisector forms right angles with the bisected segment, and right angles are congruent).

Step2: Analyze other options

• For \(\overline{FH}\cong\overline{GH}\), if \(DH\) is the perpendicular bisector of \(FG\), then \(H\) is the mid - point of \(FG\) (by the definition of a bisector), so \(\overline{FH}\cong\overline{GH}\) is incorrect because the perpendicular bisector property does not directly imply this in the context of the given problem (assuming the problem is about the relationship of the bisector to other elements in a non - trivial geometric figure where this is not a direct consequence).
• For \(\angle FDH\cong\angle DGH\), there is no reason based on the perpendicular bisector property (which mainly deals with segment congruence and right - angle congruence related to the bisected segment) to assume these angles are congruent.
• For \(\overline{DH}\cong\overline{BH}\), there is no information from the fact that \(DH\) is a perpendicular bisector of \(FG\) to support this segment congruence.

Answer:

\(\overline{FG}\cong\overline{DE}\), \(\angle DHF\cong\angle DHG\)