Anonymous

# GEOMETRY PARALLELAGRAM PROOF!?!?! help?!?

Write a two-column proof to show RSTW is a parallelogram using the method that states that if one pair of opposite sides is both parallel and congruent then the quadrilateral is a parallelogram.

RSTW has dignoals that bisect at point V

Given: <WRS is congruent to <STW and <RSW is congruent to <TWS

Prove: RSTW is a parallelogram

I am not just a slacker looking for an easy way out of work I just really do not understand this question- got all the others though lol!!

Relevance

First off, i we can prove RS = WT, RS // WT and RW = ST, RW // ST, then the figure is a parallogram

1) <RSW = <TWS by given

2) RS // WT by the Converse of Alternate Interior angle Theorem

3) <RVS = < TVW by Vertical Theorems

4) RV = VT and WV = VS by Midpoint Postulate

5) ΔRVS = ΔTVW by SAS

6) RS = WT by CPCTC

7) <RVW = <TVS by Vertical Angles Thereom

8) ΔRVW = ΔSVT by SAS

9) <RWS = <TSW by CPCTC

10) RW // ST by Converse of Alternate Interior Angle Theorem

11) RW = ST by CPCTC

12) RSWT is a parallelgram by defination of a Parallogram

Well, parallellograms have two sets of parallel sides whose length is the same (congruent). If you have two parallel segments of the same length, then (a) their ends must be the same distance apart because the segments are parallel, and (b) the segments joining the ends of the first to segments must also be parallel because if they weren't the original segments would not be congruent. Thus, the joining segments are parallel and congruent; that means all the sides are parallel and congruent so therefore you have a parallelogram.

R ------- S

\ \

\ \

W ------- T

Then what you know is that the vector RS = WT and the vector RW = ST.

You also know things like RS + ST = RT as vectors. V is your

origin. Then the midpoint of RT is (OR + OT)/2 = OX. What's

vector SX then? It's OX - OS. And XW = OW - OX.

By combining the value I found for point X with some of these other things (and other relations, like RS = OS - OR = WT = OT - OW ...) you should be able to put together a proof.