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!!
- 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
- 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
- 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
- Anonymous4 years ago
It's really interesting
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- Anonymous4 years ago