Triangle QRS is similar to triangle TUV. Using the image below, prove that lines RS and UV have the same slope. You must show all of your work to receive credit.

Question

prince1342 · Answer

attachment

michele_laino · Answer

hint:
the side SQ is 6 little squares long, whereas the side QR is also 6 little squares long, so the slope of SR is $6/6=1$
now, please do the same with the triangle TUV

prince1342 · Answer

I got 3 for all coordinates on TUV

michele_laino · Answer

hint:
what is the length of the side VT?
what is the length of the side TU?

prince1342 · Answer

both are 3

michele_laino · Answer

ok! so, slope of UV, is:
$3/3=...?$

prince1342 · Answer

That would equal 1 i believe

michele_laino · Answer

yes! correct!
so we have
$$slope = \frac{{TU}}{{TV}} = \frac{3}{3} =1$$
and
$$slope = \frac{{QR}}{{QS}} = \frac{6}{6} = 1$$

michele_laino · Answer

more precisely:
$$\begin{gathered}
  slope\;of\;UV = \frac{{TU}}{{TV}} = \frac{3}{3} = 1 \hfill \
   \hfill \
  slope\;of\;RS = \frac{{QR}}{{QS}} = \frac{6}{6} = 1 \hfill \ 
\end{gathered} $$

prince1342 · Answer

oh okay, thank you so much!