Question

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

Explanation:

Step1: Recall the definition of a perpendicular bisector

A perpendicular bisector of a line - segment divides the line - segment into two equal parts and is perpendicular to it.
Since $\overline{DE}$ is the perpendicular bisector of $\overline{FG}$ and they intersect at $H$, by the definition of a bisector, $\overline{FH}\cong\overline{GH}$.

Step2: Recall the property of perpendicular lines

Perpendicular lines form right - angles. Since $\overline{DE}\perp\overline{FG}$, $\angle DHF$ and $\angle DHG$ are right - angles. So, $\angle DHF\cong\angle DHG$ (all right - angles are congruent).

Answer:

$\overline{FH}\cong\overline{GH}$, $\angle DHF\cong\angle DHG$