## Geometry: Common Core (15th Edition)

a) Because $\overline{PQ}$ and $\overline{QR}$ are congruent, the length of $\overline{QR}$ can be determined by finding the length of $\overline{PQ}$. b) $TU=UV\longrightarrow$ definition of midpoint $8x+11=12x-1\longrightarrow$ substitute $8x+11-8x=12x-1-8x\longrightarrow$ subtrat 8x from each side $11=4x-1\longrightarrow$ combine like terms $11+1=4x-1+1\longrightarrow$ add 1 to each side $12=4x\longrightarrow$ simplify $12\div4=4x\div4\longrightarrow$ divide each side by 4 $3=x$ Substitute to find TU and UV. $TU=8x+11=8(3)+11=24+11=35$ $UV=12x-1=12(3)-1=36-1=35$ Use the segment addition postulate. $TV=TU+UV=35+35=70.$