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Give Triangle QRS ~= Triangle TUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV

Give Triangle QRS Triangle TUV QS 3v 2 And TV 7v 6 Find The Length Of QS And TV class=

Sagot :

[tex]QS\cong TV=8[/tex]

1) Since these triangles are congruent, then we can write out the following for congruent triangles have congruent sides:

[tex]\begin{gathered} QS=TV \\ 3v+2=7v-6 \\ 3v-7v=-6-2 \\ -4v=-8 \\ 4v=8 \\ \frac{4v}{4}=\frac{8}{4} \\ v=2 \end{gathered}[/tex]

2) Still based on that principle, we can plug v=2 into any of those formulas to get the measure of QS and TV. So let's pick the simpler one:

[tex]\begin{gathered} QS=3v+2 \\ QS=3(2)+2 \\ QS=6+2 \\ QS=8 \\ --- \\ TV=7(2)-6 \\ TV=14-6 \\ TV=8 \end{gathered}[/tex]

As we can see these segments are congruent.

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