Question

GJ bisects ∠FGH and is a perpendicular bisector of FH.

Triangle F G H is cut by perpendicular bisector G J. Line segments F J and J H are congruent. Angle F G J and J G H are both 30 degrees.

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.

Answer 1

Based on the information provided, we can analyze triangle FGH as follows:

1. **GJ is a perpendicular bisector of FH**: This means that GJ intersects FH at a right angle (90 degrees) and divides FH into two equal segments (FJ ≅ JH).

2. **GJ bisects ∠FGH**: This means that the angles ∠FGJ and ∠HGJ are equal. Since we know that ∠FGJ = 30 degrees, it follows that ∠HGJ = 30 degrees as well.

3. **Angles in triangle FGH**: Since GJ is perpendicular to FH, we know that ∠FGJ + ∠HGJ + ∠FGH = 180 degrees. Therefore, we need to find angle ∠FGH. We already have:
- ∠FGJ = 30 degrees
- ∠HGJ = 30 degrees

Adding these two angles gives us 30 + 30 = 60 degrees. Now we can find ∠FGH:
- ∠FGH = 180 degrees - (∠FGJ + ∠HGJ)
- ∠FGH = 180 degrees - 60 degrees = 120 degrees.

Since one of the angles (∠FGH) is greater than 90 degrees, this confirms that triangle FGH is an obtuse triangle.

4. **Congruency of sides**: Since FJ ≅ JH (because GJ is the perpendicular bisector), we can conclude that triangle FGH has at least two sides congruent, but we do not have enough information to conclude that all three sides of triangle FGH are congruent.

In summary, the correct option is:

**It is an obtuse triangle.**