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 a right triangle. it will be an acute triangle. it will be an equilateral triangle. it will be an isosceles triangle.

Explanation:

Step1: Recall property of perpendicular bisector

A point on the perpendicular bisector of a line - segment is equidistant from the endpoints of the line - segment.
Let \(P\) be a point on \(\overleftrightarrow{RT}\) other than \(S\). Since \(\overleftrightarrow{RT}\) is the perpendicular bisector of \(\overline{UV}\), we have \(PU = PV\).

Step2: Define triangle type

In \(\triangle UPV\), because \(PU = PV\), by the definition of an isosceles triangle (a triangle with at least two congruent sides), \(\triangle UPV\) is an isosceles triangle.

Answer:

It will be an isosceles triangle.