Anonymous

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

Update:

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

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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• 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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• 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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• Anonymous
3 years ago

It's really interesting

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