Question

if \\( \overline { s t } \cong \overline { s v } \\), \\( t u = a + 60 \\), and \\( u v = 4 a \\), what is \\( t u \\)?

Explanation:

Step1: Use the property of congruent segments and perpendicular bisector

Since \(\overline{ST}\cong\overline{SV}\) and \(SU\perp TV\) (implied by the right - angle symbol), by the perpendicular bisector theorem, \(TU = UV\).

Step2: Set up the equation

We know that \(TU=a + 60\) and \(UV = 4a\). So, \(a+60=4a\).
Subtract \(a\) from both sides: \(60=4a - a\), which simplifies to \(60 = 3a\).
Divide both sides by 3: \(a=\frac{60}{3}=20\).

Step3: Find the value of \(TU\)

Substitute \(a = 20\) into the expression for \(TU\): \(TU=a + 60\).
\(TU=20+60\).

Answer:

\(80\)