Given:st||uv,st=vu Prove:stw=vuw

Question

Statements	Reasons
1.	Given
2.	Given
3.	Alternate Interior Angles Thm.
∠SUT ≅ ∠WUV	4.
5.	AAS
SU ≅ WU	6.

Answer 1

Statement(Reason)

ST || UV (Given)

Angle S = Angle V (Alternate interior angle)

Angle SWT = Angle VWU (Vertically opposite Angle)

ST = VU (Given)

Therefore, based on above, we can say that the triangle STW is congruent to VUW by AAS (i.e. Angle Angle Side congruency.