Triangle HGF is a right triangle due to the perpendicular bisector creating a 90° angle at H, and also an isosceles triangle since JG bisects HF, indicating two equal angles at H and F.
To determine the best description of triangle HGF, where segment JG bisects angle HGF and is a perpendicular bisector of segment HF, and given that angle FGH=30°, we need to analyze the given information.
Since JG is a perpendicular bisector of HF, triangle HGF has a right angle at H (this is because a perpendicular line forms a 90° angle).
Thus, triangle HGF is indeed a right triangle.
The information also implies that segments JH and JF are equal in length because JG bisects HF.
Given angle FGH is 30°, which means that angle HGF must be 60° (since the angles in a triangle add up to 180°, and one angle is already 90°).
This information indicates that the triangle is not only a right triangle but also an isosceles triangle, with two angles equal.
The probable question may be:
Segment JG bisects angle HGF and is a perpendicular bisector of segment HF. angle FGH=30°.
What best describes triangle HGF?
A. It is a right triangle.
B. It is an obtuse triangle.
C. It is an isosceles triangle.
D. It is an equilateral triangle.