Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

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

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!!

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  • 1 decade ago
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    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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  • 1 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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  • 1 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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  • Anonymous
    3 years ago

    It's really interesting

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  • Anonymous
    3 years ago

    it depends...

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