Question

de 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. (2 points) ∠dhf ≅ ∠dhg fg ≅ de dh ≅ eh ∠fdh ≅ ∠dgh fh ≅ gh

Explanation:

Step1: Analyze the property of perpendicular bisector

Since $\overline{DE}$ is a perpendicular bisector of $\overline{FG}$, then $\overline{FH}\cong\overline{GH}$ (by the definition of a bisector: a bisector divides a segment into two congruent parts).

Step2: Analyze the right - angle property

Also, $\angle DHF$ and $\angle DHG$ are right angles (because $\overline{DE}$ is perpendicular to $\overline{FG}$). All right angles are congruent, so $\angle DHF\cong\angle DHG$.

Step3: Analyze other options

• $\overline{FG}\cong\overline{DE}$: There is no information given to suggest that the lengths of $\overline{FG}$ and $\overline{DE}$ are equal.
• $\overline{DH}\cong\overline{EH}$: There is no information given to suggest that $H$ bisects $\overline{DE}$.
• $\angle FDH\cong\angle DGH$: There is no information given to suggest that these two angles are congruent.

Answer:

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