Question 1210360
<pre>
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.

{{{drawing(400,240,-4,6, -1,5,

line(-3,0,5,0),
line(0,0,-2,4),
line(-2,4,3,4),
line(3,4,5,0),
line(-2,4,5,0),

locate(-3,0,X),
locate(0,0,R),
locate(5,0,S),
locate(3,4+.3,T),
locate(-2-.2,4+.3,V),

red(arc(0,0,2,-2,116,180), arc(5,0,2,-2,116,180)),

green(arc(5,0,4,-4,150,180), arc(-2,4,4,-4,330,360),

arc(5,0,4.5,-4.5,150,180), arc(-2,4,4.5,-4.5,330,360))


 )}}}

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</pre>