Question

cj bisects \\( \angle fgh \\) and is a perpendicular bisector of \\( \overline{fh} \\). what is true of triangle fgh? it is an obtuse triangle. it has exactly 3 congruent sides. it has exactly 2 congruent sides. it is a right triangle.

Explanation:

Step1: Use the property of perpendicular bisector

Since \(GJ\) is the perpendicular bisector of \(FH\), we know that \(FG = GH\) (by the property that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment).

Step2: Analyze the options

• An obtuse triangle has one angle greater than \(90^{\circ}\). There is no information to suggest this.
• A triangle with exactly 3 congruent sides (equilateral triangle) has all angles equal to \(60^{\circ}\). Here, the angle at \(G\) is \(60^{\circ}\) (since it is bisected into two \(30^{\circ}\) angles), but we don't know about the other angles being \(60^{\circ}\).
• A right - triangle has one angle equal to \(90^{\circ}\). There is no information to suggest this.
• Since \(FG = GH\), triangle \(FGH\) has exactly 2 congruent sides.

Answer:

It has exactly 2 congruent sides.