# geometry proofs parallelagrams PLEASE 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!!

### 5 Answers

- 1 decade agoFavorite Answer
Let quadrilateral RSTW, have sides RW parallel and equal to ST say. Diagonals are RT and SW.

Then triangles WRS, and STW are congruent

as RW=ST, SW is common to both, and alternate angles RWS=WST

So RS =TW.

Triangles SRT and WRT are congruent as

RS=TW, ST=RW, and TR common to both

Hence alternate angles SRT = RTW

So RS is parallel to WT

so RSTW is a parallelogram

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- davec996Lv 41 decade ago
It's been a long time, and we probably speak different (mathematical) languages -- so I'll refer to the document listed as the source -- you'll have to translate it into what you know. OK -- lets go. (What's a 2 column proof?)

RSTW is a quadrilateral. -- given.

First lets prove that RS is parallel with WT. (= means congruent)

∠RSW = ∠TWS -- given

∠RSW = ∠TWS are alternate angles made by the intersection of line WS with lines RS and WT - given

RS is parallel with WT -- source-proposition 27.

now show RS = WT

RV=VT - given WS & RT are bisected at V

WV=VS - given WS & RT are bisected at V

∠RVS = ∠WVT -- source-Prop 15

∆RVS = ∆WVT -- side-angle-side

RS = WT -- congruent triangles

RSTW is a parallelogram -- If one pair of opposite sides is both parallel and congruent then the quadrilateral is a parallelogram -QED

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- Nishant PLv 41 decade ago
since the <rsw=<tws then you could say that side RS is parallel to side WT

then you could say that <RWS=<WST

then you could say that WS=WS

then you've coungrent traingle by ASA b/c you already 've those 2 parirs of coungrent <s and now you added another one ans now you 've congrent triangles.

then you could say that opposite are coungrent and parallel b/c corresponding parts of congrent triangles are congrent and therefore theyr are congrent and sine you have congrent <s you could aslo say thery are parallel by PAI

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- Anonymous4 years ago
It's really interesting

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- Anonymous4 years ago
it depends...

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