Question

if $\angle rsu \cong \angle tsu$, $ru = v + 18$, and $tu = 3v$, what is the value of $v$?
$v = \square$

Explanation:

Step1: Identify congruent segments

Since $\angle RSU \cong \angle TSU$, and $SU$ is an angle bisector, with $UR \perp SR$ and $UT \perp ST$, by the Angle Bisector Theorem, $RU = TU$.

Step2: Set up equation

Substitute given expressions:
$v + 18 = 3v$

Step3: Solve for $v$

Subtract $v$ from both sides:
$18 = 2v$
Divide by 2:
$v = \frac{18}{2}$

Answer:

$9$