Where can the perpendicular bisectors of an acute triangle intersect?
I. inside the triangle
II. on the triangle
III. outside the triangle
(1 point)
Responses
I only
I only
III only
III only
I or III only
I or III only
I, II, or III
I, II, or III
I, II, or III
no its only I
I apologize for the confusion. You are correct, the perpendicular bisectors of an acute triangle can only intersect inside the triangle.
The perpendicular bisectors of an acute triangle can intersect at different locations. In this case, they can intersect at any of the given options: inside the triangle (I), on the triangle (II), or outside the triangle (III). So the correct answer is I, II, or III.
To determine where the perpendicular bisectors of an acute triangle can intersect, let's understand what a perpendicular bisector is. A perpendicular bisector is a line that divides a line segment into two equal parts and forms a right angle with the line segment.
In the case of an acute triangle, the perpendicular bisectors of the triangle's sides will always intersect at a single point. This point is called the circumcenter of the triangle. The circumcenter is the center of a circle that passes through all three vertices of the triangle.
Therefore, the correct choice is III only - the perpendicular bisectors of an acute triangle will only intersect outside the triangle at the circumcenter.