Question

if \\( \overline{tu} \cong \overline{uv} \\) and \\( sv = 16 \\), what is \\( tv \\)?

Explanation:

Step1: Apply the Perpendicular Bisector Theorem

Since \( \overline{TU}\cong\overline{UV}\) and \( US\perp TV\), 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), we know that \( TS = SV\).

Step2: Calculate \( TV\)

We know that \( TV=TS + SV\). Since \( TS = SV\) and \( SV = 16\), then \( TV=16 + 16\).

Answer:

\(32\)