SOLUTION: A quadrilateral, STVR has an exterior angle VRX. Given angle XRV is congruent to angle RST, and angle RSV is congruent to angle TVS, prove that RSTV is a parallelogram.

Given:
A quadrilateral, STVR 
exterior angle VRX.  
angle XRV is congruent to angle RST.
angle RSV is congruent to angle TVS, 

To prove:
RSTV is a parallelogram.



1. angle XRV is congruent to angle RST  |  1. given

2. VR is parallel to TS                 |  2. If a transversal, XS, intersects
                                        |     two coplanar lines, VR and TS, and
                                        |     a pair of corresponding angles--
                                        |     namely angles XRV and RST -- are
                                        |     congruent, then the two coplanar
                                        |     lines, VR and TS, are parallel. 
                                        
3. angle RSV is congruent to angle TVS  |  3. given

4. VT is parallel to RS                 |  4. If a transversal, VS, intersects
                                        |     two coplanar lines, VT and RS, and
                                        |     the alternate interior angles, RSV
                                        |     and TVS are congruent, then the
                                        |     the two coplanar lines, VT and RS,
                                        |     are parallel.  

5. RSTV is a parallogram.               |  5. The definition of parallelogram:      
                                        |     A quadrilateral with each pair of
                                        |     opposite sides, (VR and TS), and
                                        |     (VT and RS), parallel. 
                                              

Edwin