Question

If RT bisects SU find each measure geometry perpendicular & angle bisectors

Answer 1

Since RT bisects SU, we can imply that

`\begin{gathered} RT\text{ bisects }SU \\ \Rightarrow SV=VU \\ \text{and} \\ VU=5 \\ \Rightarrow SV=5 \end{gathered}`

SV=5

Notice that, since SV=VU, triangles VST and VUT are congruent triangles due to the SAS postulate; therefore,

`\begin{gathered} \Delta\text{VST}\cong\Delta VUT \\ \Rightarrow ST\cong UT \\ \Rightarrow ST=23 \end{gathered}`

ST=23.

Similarly, triangles VSR and VUR are congruent due to the SAS postulate (both share side RV, have a right angle, and SV=UV); thus,

`\begin{gathered} \Delta\text{VSR}\cong\Delta\text{VUR} \\ \Rightarrow SR\cong UR \\ \Rightarrow UR=8 \end{gathered}`

UR=8

Finally, notice that

`\begin{gathered} SU=SV+VU \\ \Rightarrow SU=2VU\to SV\cong VU \\ \Rightarrow SU=2\cdot5=10 \\ \Rightarrow SU=10 \end{gathered}`

Thus, SU=10