Question

rt is a perpendicular bisector of uv. what is true of any triangle created by points u, v, and any point on rt other than s? it will be an equilateral triangle. it will be a right triangle. it will be an acute triangle. it will be an isosceles triangle.

Explanation:

Step1: Recall the property of perpendicular bisector

A point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment. So, if we take any point \(P\) on \(\overleftrightarrow{RT}\) (other than \(S\)), then \(PU = PV\) (by the perpendicular - bisector theorem: If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment).

Step2: Define the triangle

In \(\triangle PUV\), since \(PU = PV\), a triangle with two sides equal is an isosceles triangle.

Answer:

It will be an isosceles triangle.