Theoreme de Thales Exercices Corriges
August 18, 2022 | Author: Anonymous | Category: N/A
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^bçorâea na ^b`lâs Axarcgcas corrghçs Sokt `dornçs n`ks catta igcba =
Axarcgcas 0, 4 at 3 = c`lculs na lokhuaurs
p`rt`ha n‗uk saheakt s`ks râhla hr`nuça > = p`rt`ha Axarcgca Axarcgca 1 = prodlâea `vac plusgaurs cokighur`tgoks na ^b`lâs Axarcgca 9 = `hr`kngssaeakt n‗uka ighura, nçtaregk`tgok n‗uk i`ctaur n‗`hr`kngssaeakt n‗`hr`kngssaeakt
T`ppal = ^bçorâea na ^b`lâs Sogakt naux nrogtas at sçc`ktas ak uk pogkt . Sogakt naux pogkts at na , ngstgkcts na . Sogakt naux pogkts at na , ngstgkcts na .
Sg las nrogtas at sokt p`r`llâlas, `lors n‗`prâs la tbçorâea na ^b`lâs, ok ^b`lâs, ok ` las çh`lgtçs sugv`ktas =
^rogs cokighur`tgoks sokt akvgs`ha`dlas =
Las pogkts , at n`ks cat ornra. Las pogkts , at n`ks cat ornra.
sokt `lghkçs
Las pogkts , at sokt `lghkçs Las pogkts , at sokt `lghkçs n`ks cat ornra. n`ks cat ornra. sokt `lghkçs Las pogkts , at sokt `lghkçs Las pogkts , at sokt `lghkçs n`ks cat ornra.
n`ks cat ornra.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
0
Tae`rqua geport`kta = Las lokhuaurs nas cþtçs nu trg`khla sokt proportgokkallas `ux lokhuaurs nas cþtçs nu trg`khla . N`ks las cokngtgoks cg-nassus, ok paut nokc prçsaktar l` noudla çh`lgtç sous l` iorea n‗uk t`dla`u na proportgokk`lgtç =
Cþtçs nu trg`khla
Cþtçs portçs p`r l` nrogta
Cþtçs portçs p`r l` nrogta
Cþtçs portçs p`r las nrogtas p`r`llâlas p`r`llâlas
Cþtçs nu trg`khla
@ quog sart la tbçorâea na ^b`lâs ? æ c`lcular uka lokhuaur æ p`rt`har uk saheakt at pl`car sur uk saheakt s aheakt uk pogkt ak raspact`kt uk r`pport nokkç æ `hr`kngr ou rçnugra uka ighura
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
4
Axarcgca 0 ( 0 qua uast stgg ok)
K g va va` `u = i`c i`cgg la
Sogt l` ighura cg-coktra.
Ok s`gt qua las nrogtas at sokt p`r`llâlas at qua , at .
C`lcular .
Corractgok na l‗axarcgca 0
@k`lysoks tout n‗`dorn l` ighura at rçc`pgtuloks las gkiore`tgoks iourkgas p`r l‗çkokcç.
at N‗`prâs l` ighura cg-coktra, cg-coktra, las nrogtas sokt sçc`ktas ak .
N‗`prâs l‗çkokcç, ok s`gt p`r `gllaurs qua qua at sokt p`r`llâlas. Akigk, ok s`gt qua =
Vroposoks nçsore`gs uka corractgok nçt`gllça, çt`pa p`r çt`pa, na l‗axarcgca.
0âra çt`pa = = Ok rapâra l` cokighur`tgok na ^b`lâs. ^b`lâs.
Ok s`gt qua = 0) las nrogtas at sokt sçc`ktas ak (n‗`prâs l` ighura) ighura) l‗çkokcç) 4) las nrogtas at sokt p`r`llâlas (n‗`prâs l‗çkokcç)
L` cokighur`tgok proposça rçiâra nokc æ l` 0âra cokighur`tgok eaktgokkça n`ks la r`ppal. Ak aiiat, las pogkts , at sokt `lghkçs n`ks cat ornra, at las pogkts , at sokt `lghkçs n`ks cat ornra.
4âea çt`pa = Ok prçcgsa la tbçorâea `uqual ok v` i`gra `ppal.
Nokc, n‗`prâs la tbçorâea na ^b`lâs, ok ` las çh`lgtçs sugv`ktas sugv`ktas = =
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
3
3âea çt`pa = Ok `pplgqua la tbçorâea na ^b`lâs ak prak`kt la sogk na dgak çcrgra las çh`lgtçs.
>âea çt`pa = Ok raepl`ca las lokhuaurs cokkuas p`r laurs easuras raspactgvas, axprgeças n`ks l`
eíea ukgtç. C‗ast-æ-ngra, C‗ast -æ-ngra, ak raepl`è`kt las lokhuaurs cokkuas p`r laurs easuras raspactgvas,
1âea çt`pa = Ok gsola l‗çh`lgtç utgla pour rçsounra l‗çqu`tgok.
V`r coksçquakt, ok ` = Gl i`ut toumours vagllar æ çcrgra uka ir`ctgok sous s`
iorea
N‗o÷, ak utglgs`kt la pronugt ak crogx = crogx =
L` easura na l` lokhuaur « toeda musta º (gl s‗`hgt n‗uk koedra nçcge`l), nokc ok paut `ussg çcrgra = ,
âea
9
çt`pa = Ok cokclut.
L` lokhuaur nu saheakt , kotça , ast çh`la æ .
Tae`rquas = N`ks cat axarcgca, gl k‗ast prçcgsç `ucuka ukgtç na lokhuaur nokc gl k‗y ` p`s p`s lgau n‗çcrgra qualqua ukgtç na lokhuaur qua ca sogt (ce, e, je…). je…). Sgkok, ca sar`gt uka arraur ! Ok vogt nokc dgak læ l‗geport`kca na lgra `ttaktgvaeakt l‗çkokcç at l` ighura, ighura , pugsqua l‗uk l‗ uk coeea l‗`utra pauvakt geposar uka ukgtç na lokhuaur at p`r coksçquakt gknugra uk cart`gk rçsult`t.
Axarcgca 4
K g va va` `u = i`c i`cgg la
( 4 qua uast stgg oks) Sur l` ighura cg-coktra, ok ` kotç ngiiçraktas lokhuaurs cokkuas. Ok s`gt p`r `gllaurs qua las nrogtas at sokt p`r`llâlas. 0- C`lcular . 4- Ak nçnugra l` lokhuaur nu saheakt
.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
>
Corractgok na l‗axarcgca 4
0- N‗`prâs l` ighura, ok s`gt qua las nrogtas nrogtas at sokt sçc`ktas ak
.
Ok s`gt p`r `gllaurs, n‗`prâs l‗çkokcç, qua las nrogtas at sokt p`r`llâlas. Nokc, n‗`prâs la tbçorâea na ^b`lâs, ok ` las çh`lgtçs sugv`ktas sugv`ktas = =
C‗ast-æ-ngra, C‗ast -æ-ngra, ak raepl`è`kt las lokhuaurs cokkuas p`r laurs easuras raspactgvas,
N‗o÷ l‗çh`lgtç = l‗çh`lgtç =
@ l‗`gna n‗uk pronugt ak crogx, ok odtgakt nokc qua = qua =
L` lokhuaur nu saheakt , kotça , ast çh`la æ eâtras.
4-
nokc . l‗çh`lgtç sugv`kta = sugv`kta = . V`r coksçquakt,
N‗o÷, ak raepl`è`kt las lokhuaurs cokkuas p`r laurs easuras raspactgvas,
.
La saheakt easura 9 eâtras.
Tae`rqua = N`ks cat axarcgca, l‗ukgtç na lokhuaur ast coeeuka æ tous las saheakts pugsqu‗gl s‗`hgt nu eâtra. Gl ka i`ut m`e`gs oudlgar n‗axprgear cb`cuka nas easuras n`ks l` eíea ukgtç `ig `igk k na ka p`s i`ussar las c`lc c`lculs. uls.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
1
Axarcgca 3 ( 4 quast uastgg oks)
K g va va`u `u = eoy oya ak
N`ks las naux c`s sugv`kts, las nrogtas at sokt p`r`llâlas. C`lcular l` lokhuaur .
C`s k¶ 0 =
C`s k¶ 4 =
Corractgok na l‗axarcgca 3
C`s k¶0 =
N‗`prâs l` ighura, las nrogtas nrogtas at sokt sçc`ktas ak
.
Ok s`gt p`r `gllaurs, n‗`prâs l‗çkokcç, qua las nrogtas at sokt p`r`llâlas. Nokc, n‗`prâs la tbçorâea na ^b`lâs, ok ` las çh`lgtçs sugv`ktas sugv`ktas = =
C‗ast-æ-ngra, C‗ast -æ-ngra, ak raepl`è`kt las lokhuaurs cokkuas p`r laurs easuras raspactgvas,
N‗o÷ l‗çh`lgtç = l‗çh`lgtç =
@ l‗`gna n‗uk pronugt ak crogx, ok odtgakt nokc qua = qua =
L` lokhuaur ast çh`la æ .
C`s k¶4 =
N‗`prâs l` ighura, las nrogtas at sokt sçc`ktas ak
.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
9
Ok s`gt p`r `gllaurs, n‗`prâs l‗çkokcç, qua las nrogtas at sokt p`r`llâlas. Nokc, n‗`prâs la tbçorâea na ^b`lâs, ok ` las çh`lgtçs sugv`ktas sugv`ktas = =
C‗ast-æ-ngra, C‗ast -æ-ngra, ak raepl`è`kt las lokhuaurs cokkuas p`r laurs easuras raspactgvas,
Ak aiiat, . N‗o÷ l‗çh`lgtç = l‗çh`lgtç =
@ l‗`gna n‗uk pronugt ak crogx, ok odtgakt nokc qua =
@ttaktgok ! Gl ka i`ut p`s oudlgar las p`raktbâsas.
Tçsolvoks l‗çqu`tgok
.
c‗ast-æ-ngra . , c‗ast-æ-ngra çqugv`ut æ ⏟ ⏟
N‗o÷ = N‗o÷ = @gksg,
.
.
Vour supprgear las p`raktbâsas, ok utglgsa l` ngstrgdutgvgtç na l` eultgplgc`tgok sur l‗`nngtgok = l‗`nngtgok =
L` lokhuaur ast çh`la æ , ,.
uastgg ok) Axarcgca > ( 0 quast
K g va va`u `u = eoy oya ak
^r`car uk saheakt . Vl`car la pogkt sur tal qua
, s`ks râhla hr`nuça.
Corractgok na l‗axarcgca >
^r`èoks uk saheakt pugs pl`èoks la pogkt sur tal qua
, s`ks râhla hr`nuça.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
8
0- Coeeakèoks p`r tr`car uk saheakt na lokhuaur qualcokqua. 4- ^r`èoks nçsore`gs uka naeg-nrogta , qua kous `lloks hr`nuar sorta æ odtakgr saheakts na lokhuaur gnaktgqua.
rçhulgâraeakt æ l‗`gna nu coep`s, coep`s, na
3- Vl`èoks norçk`v`kt las pogkts at sur l` naeg-nrogta tals qua at .
>- ^r`èoks e`gktak`kt l` nrogta p`r`llâla æ at p`ss`kt p`r . Catta nrogta coupa la saheakt ak uk pogkt qua kous
`ppallaroks . Gl s‗`hgt nu pogkt racbarcbç. racbarcbç.
Pualquas axplgc`tgoks pour dgak coepraknra = Las nrogtas at sokt sçc`ktas ak . N‗`utra p`rt, p`r cokstructgok, las nrogtas at sokt p`r`llâlas. ^outas las cokngtgoks sokt p`r coksçquakt rçukgas pour pouvogr pouvogr `pplgquar la tbçorâea na ^b`lâs. N‗`prâs la tbçorâea na ^b`lâs, ^b`lâs, ok ` las çh`lgtçs sugv`ktas = ^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
2
Or, p`r cokstructgok, ok ` l‗çh`lgtç sugv`kta = sugv`kta =
C‗ast-æ-ngra C‗ast -æ-ngra =
V`r coksçquakt, ok odtgakt qua =
C‗ast-æ-ngra C‗ast -æ-ngra =
Gl ak rçsulta, `prâs uk pronugt ak crogx, qua =
Ok ` nokc dgak pl`cç la pogkt tal qua .
Axarcgca 1 ( 0 qua uast stgg ok)
K g va va` `u = ng ii iigg cgla
ast uk tr`pâza na d`sas at at na caktra . Ok `ppalla M la pogkt na cokcours nas nrogtas at . Coep`rar las r`pports na lokhuaurs at .
Corractgok na l‗axarcgca 1
ast uk tr`pâza na d`sas at at na caktra . Ok `ppalla M la pogkt na cokcours nas nrogtas at . Coeeakèoks p`r tr`car l` ighura.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
7
0âra çt`pa = Cbarcboks æ gnaktgigar la r`pport na lokhuaurs
.
N‗uka p`rt, p`r p`r cokstructgok, las nrogtas at sokt sçc`ktas ak . N‗`utra p`rt, coeea p`rt, coeea ast uk tr`pâza na d`sas
at , las nrogtas at sokt p`r`llâlas.
V`r coksçquakt, n‗`prâs la tbçorâea na ^b`lâs, ok ` l` noudla çh`lgtç sugv`kta = sugv`kta =
4âea çt`pa = Cbarcboks æ gnaktgigar la r`pport na lokhuaurs
.
N‗uka p`rt, p`r p`r cokstructgok, ast la caktra nu tr`pâza nokc ast la pogkt n‗gktarsactgok nas ng`hok`las at . @utraeakt ngt, las nrogtas at sokt sçc`ktas ak . N‗`utra p`rt, coeea ast uk tr`pâza na d`sas
at , las nrogtas at sokt p`r`llâlas.
V`r coksçquakt, n‗`prâs la tbçorâea na ^b`lâs, ok ` l` noudla çh`lgtç sugv`kta = sugv`kta =
3âea çt`pa = Coep`roks las r`pports na lokhuaurs at .
N‗`prâs ca qug prçcâna, ok ` = ` =
at
at
Ok ` nokc ak p`rtgculgar =
Gl s‗aksugt qua = qua =
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
06 06
Axarcgca 9 ( 4 qua uast stgg oks)
K g va va` `u = i`c i`cgg la
0- Vourquog la trg`khla cg-coktra `hr`kngssaeakt nu trg`khla ?
ast-gl
uk
4- Nçtaregkar la i`ctaur n‗`hr`kngssaeakt. n‗`hr`kngssaeakt.
Corractgok na l‗axarcgca 9
T`ppal = @hr`kngssaeakt ou rçnuctgok n‗uka ighura Qka ighura ast uka TÇNQC^GOK ou uk @HT@KNGSSAEAK^ n‗uka `utra ighura = sg las `khlas na okt las eíeas easuras qua caux na ou sg toutas las lokhuaurs na l` ighura sokt proportgokkallas `ux lokhuaurs na l` ighura
La I@C^AQT na rçnuctgok ou n‗`hr`kngssaeakt corraspokn `u coaiigcgakt na proportgokk`lgtç . Sg , ok ` uk `hr`kngssaeakt. Sg , ok ` uka rçnuctgok.
Tae`rqua = Lorsqua ast uka rçnuctgok ou uk `hr`kngssaeakt na , at sokt ngtas SAEDL@DLAS. 0- Eoktroks qua la trg`khla ast uk `hr`kngssaeakt nu trg`khla
.
0âra nçeokstr`tgok possgdla =
N‗uka p`rt,
at , nokc̄
N‗`utra p`rt, n‗`prâs la con`ha na l` ighura, las trg`khlas
sokt raspactgvaeakt ract`khlas ak at , nokc ̄ . Akigk, las nrogtas at sokt toutas las naux parpakngcul`gras æ uka eíea nrogta, l` nrogta , nokc las nrogtas at sokt p`r`llâlas aktra allas. allas . Las `khlas at
at̄ sokt `lors corraspokn`kts. Nokc ̄.
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
00 00
Ak rçsueç, las trg`khlas at sokt saedl`dlas pugsqu‗gls okt las eíeas easuras n‗`khlas. @utraeakt ngt, la trg`khla ast uk `hr`kngssaeakt nu trg`khla
.
4âea nçeokstr`tgok possgdla =
Vroprgçtç = Sogakt naux nrogtas at sçc`ktas ak uk pogkt . Sg at sokt naux pogkts na , ngstgkcts na , sg at sokt naux pogkts na , ngstgkcts na , at sg las nrogtas
at sokt p`r`llâlas, `lors la trg`khla
ast uka rçnuctgok ou uk `hr`kngssaeakt nu trg`khla .
N‗uka p`rt, las las nrogtas at sokt sçc`ktas ak N‗`utra p`rt,
.
at .
at sokt toutas naux parpakngcul`gras æ uka eíea nrogta, l` nrogta nokc las nrogtas at sokt p`r`llâlas aktra allas.
Akigk, n‗`prâs la con`ha na l` ighura, las nrogtas
V`r coksçquakt, la trg`khla
ast uk `hr`kngssaeakt nu trg`khla
.
4- Nçtaregkoks la i`ctaur n‗`hr`kngssaeakt. n‗`hr`kngssaeakt. N‗`prâs l` quastgok prçcçnakta, la trg`khla ast uk `hr`kngssaeakt nu trg`khla . Nokc las lokhuaurs na N‗`prâs la tbçorâea na ^b`lâs, ok ^b`lâs, ok ` las çh`lgtçs sugv`ktas = sokt proportgokkallas `ux lokhuaurs na . N‗`prâs
Or, n‗`prâs l` ighura, at . Nokc =
V`r uk pronugt ak crogx, ok ` =
V`r coksçquakt, la trg`khla ast uk `hr`kngssaeakt nu trg`khla
p`r la i`ctaur n‗`hr`kngssaeakt .
^b`lâs – – Axarcgcas Axarcgcas corrghçs ^bçorâea na ^b`lâs © SOS NAYOGTS COTTGHAS (e`rqua nçposça)
04 04
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