Question

if ∠sut ≅ ∠suv and st = 59, what is sv? sv =

Explanation:

Step1: Apply the Angle - Bisector and Congruent Angles Property

Since \( \angle SUT\cong\angle SUV\), and \(SV\perp UV\), \(ST\perp UT\). By the Angle - Bisector Theorem (in the form that if a point is on the bisector of an angle and is equidistant from the sides of the angle), the distances from a point \(S\) to the two sides of the angle \(\angle VUT\) are equal.

Step2: Relate the lengths of \(SV\) and \(ST\)

The length \(SV\) is the distance from point \(S\) to side \(UV\), and the length \(ST\) is the distance from point \(S\) to side \(UT\). Given \(ST = 59\).

Answer:

\(59\)