Question

a maintenance crew wants to build a shed at a location that is the same distance from each path. where should the shed be located? justify your answer with a diagram. a. the point of intersection of the angle bisectors is equidistant from the sides of the triangle, which represent the paths. the shed should be built at this intersection point. b. the point of intersection of the perpendicular bisectors is equidistant from the sides of the triangle, which represent the paths. the shed should be built at this intersection point. c. draw a line segment from each vertex to the midpoint of the opposite path. the shed should be built at the intersection point of these three segments.

Explanation:

The problem requires a point equidistant from three paths forming a triangle. The incenter (intersection of angle bisectors) is equidistant from all sides of a triangle, which matches the requirement. Option A describes this property correctly.

Answer:

A. The point of intersection of the angle bisectors is equidistant from the sides of the triangle, which represent the paths. The shed should be built at this intersection point