Question

1 fill in the blank 0 points if $overline{rt}$ bisects $overline{su}$, find each measure. if $overline{rt}$ bisects $overline{su}$, find each measure. st = type your answer.. ru = type your answer.. sv = type your answer.. su = type your answer..

Explanation:

Step1: Use Pythagorean theorem for $ST$

In right - triangle $SVT$, $SV = 8$, $VT=23$. By the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = SV$, $b = VT$ and $c = ST$. So $ST=\sqrt{8^{2}+23^{2}}=\sqrt{64 + 529}=\sqrt{593}$.

Step2: Use Pythagorean theorem for $RU$

In right - triangle $RVU$, $RV = 8$, $VU = 23$. By the Pythagorean theorem, $RU=\sqrt{8^{2}+23^{2}}=\sqrt{593}$.

Step3: Find $SV$

Given in the figure, $SV = 8$.

Step4: Find $SU$

Since $SV = 8$ and $VT$ bisects $SU$, then $SU=2\times SV$. So $SU = 16$.

Answer:

$ST=\sqrt{593}$
$RU=\sqrt{593}$
$SV = 8$
$SU = 16$