MHB Need help with parallelogram proof

[sc00t34]

Hello, we are learning about similar triangles and this was a problem. So I know that opposite sides of a parallelogram are congruent as are opposite angles, so I can establish similarity with triangles WYS and STW, but I don't understand how that proves SX x YW = SV x WT because the proportions don't match up when I compare similar triangles for their corresponding parts.

Any help is greatly appreciated... am I on the right track?

This is what I have so far. See attached image.

Statement Reason

1. WYST is Parallelogram. 1. Given
2. angle Y and angle T are congruent. 2. Def of parallelogram, opposite angles congruent.
3. WT and YS congruent, WY and TS congruent. 3. Def of parallelogram, opposite sides congruent.
4. WYS and STW are similar. 4. SAS
?

 

[Opalg]

The similar triangles that you need to look at are $SXY$ and $SVT$. Then use the fact that opposite sides of the parallelogram are equal.