Question

1. Given ΔQRS (is congruent to) ΔTUV, QS = 3v + 2 and TV = 7v - 6, find the length of QS and TV. Provide a detailed response below, please. I was not provided with a picture, unfortunately.

Answer 1

So, we know the 2 triangles are congruent, that means that all complementary sides are congruent too. Draw out the triangle, make it look equal to each other, and put down the respective names down, IN ORDER, for both triangle. Then, you will see that QS and TV are complementary to each other, meaning they are congruent to each other. So, we can set their two equation equal to each other. Equation: 3v + 2 = 7v - 6. Now it's all algebra, solve for v, you should get 2. Now, we plug it back in for one of the equations (either one is fine because they are congruent to each other already), you should get 8 as your answer. I hope this helps!

Answer 2

Because ΔQRS is congruent to ΔTUV, the the segments GS and TV are also congruent due to the letter order (Q and T are first and S and V are 3rd.) Since they are congruent QS=TV. So 3v + 2 = 7v - 6

Work: 
3v + 2 = 7v - 6
      +6          +6
3v + 8=7v
-3v       -3v
8 = 4v
4      4
2 = v

3(2) + 2 = GS
6+2 = GS
8 = GS

7(2) - 6 = TV
14-6=TV
8 = TV

Final Answer: 8=QS and 8=TV