Answer:
2 : 7
Step-by-step explanation:
Draw a line parallel to RS through U. Label its intersection with TM as point X. This will create triangle UMX congruent to triangle RMV by the ASA postulate. (Vertical angles at M are congruent; MR = MU by definition: and angles VRM and XUM are alternate interior angles at a transversal of parallel lines.) Then UX = RV by CPCTC.
The line UX has also created similar triangles TUX and TSV. Their scale factor is TU : TS = 2 : (2+3) = 2 : 5. The sides UX : SV have the same scale factor, 2 : 5.
From above, we know that UX = RV, which tells us the scale factor of RV : SV is 2 : 5. Thus ...
RV:RS = RV:(RV+SV) = 2:(2+5)
RV:RS = 2:7
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Comment on the solution
I had to draw the attached figure to see what the ratio was. Then I had to figure out a way to show why. The congruent angles at M and the equal sides RM and UM offered a clue as to how to do it.
