Question

gj bisects ∠fgh and is a perpendicular bisector of fh. what is true of triangle fgh? it is a right triangle. it is an obtuse triangle. it has exactly 2 congruent sides. it has exactly 3 congruent sides.

Explanation:

Step1: Recall properties of perpendicular bisector

Since $\overline{GJ}$ is a perpendicular bisector of $\overline{FH}$, we know that $FG = GH$ (any point on the perpendicular bisector of a line - segment is equidistant from the endpoints of the line - segment).

Step2: Analyze angle - bisector information

$\overline{GJ}$ bisects $\angle FGH$. Let $\angle FGJ=\angle JGH = 30^{\circ}$, but this angle - measure information is not necessary to determine the side - length relationship. The key is the perpendicular - bisector property.

Answer:

It has exactly 2 congruent sides.