Modern Geometry: Proving Angles Congruent

**If ***WS *= *WT *and *RS *= *ST *= *TU*, with *R-S-T-U*, prove that ∠*RWS *http://i42.tinypic.com/1222p20.gif∠*TWU***.**

http://i39.tinypic.com/ehmz5e.jpg

**My work so far:**

Proof:

Given: *WS *= *WT *and *RS *= *ST *= *TU*, with *R-S-T-U*

Given that R-S-T-U, we know R-S-T, S-T-U, R-S-U, and R-T-U.

∠WST http://i42.tinypic.com/1222p20.gif∠WTS by the Isosceles Triangle Theorem.

m∠WST = m∠WTS by CPCF (Congruent Parts of Congruent Figures)

m∠WSR + m∠WST = 180, and m∠WTU + m∠WTS = 180.

m∠WSR = m∠WTU by algebra

∠WSR http://i42.tinypic.com/1222p20.gif∠WTU, and therefore,

Triangle WSR http://i42.tinypic.com/1222p20.gif Triangle WTU by SAS.

And thus, **∠***RWS *http://i42.tinypic.com/1222p20.gif∠*TWU *by CPCF.

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Am I even close to having a legitimate proof? I'm pretty sure there is something missing since I did not use the given betweenness relation of R-S-T-U.

Any corrections/suggestions, tips/help is greatly appreciated. Thank you very much for your time.(Hi)