What is the length of segment TQ?
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Answer: 14
Step-by-step explanation:
We know that [tex]\triangle SRV \con \triangle QRV[/tex] by SAS, so this means [tex]QV=SV[/tex] by CPCTC. Hence, [tex]4x-1 \longrightarrow x=4[/tex].
We also know that [tex]\triangle STR \cong \triangle QTR[/tex] by SAS, so this means [tex]TS=TQ[/tex] by CPCTC. Since [tex]TS=3x+2=3(4)+2=14[/tex], TQ=14.
Check the picture below.
we know that SR = RQ, we also know the angles at the point R are four right angles, triangles TRS and TRQ are sharing the same side of TR, that makes those two triangles congruent triangles by right-triangles LL theorem.
Likewise, triangles VRS and VRQ are sharing the side RV and thus those triangles are also congruent triangles by right-triangles LL theorem.
due to congruent triangles, then TQ = 3x+2 and 4x-1 = 15.