Teorema del baricentro del triangolo

Questa voce o sezione sull'argomento geometria non cita le fonti necessarie o quelle presenti sono insufficienti.

Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Segui i suggerimenti del progetto di riferimento.

Il teorema del baricentro del triangolo fa parte della geometria elementare e consegue dal teorema di Talete.

Enunciato

Le mediane di un triangolo si incontrano in uno stesso punto, il baricentro. Ogni mediana resta divisa dal baricentro in due parti e quella cui appartiene il vertice è doppia dell'altra.

Dimostrazione

Siano AM, BN e CP le mediane del triangolo ABC e G il punto in cui AM incontra BN. Si dimostra all'inizio che AG=2GM e BG=2GN, poi che anche la mediana CP passa per il punto G.

Il segmento che unisce i punti medi M e N è parallelo al lato AB e pari alla sua metà per una proposizione che discende, anche se indirettamente, dal teorema di Talete. Con lo stesso ragionamento se Q e R sono i punti medi di AG e BG allora il segmento QR è parallelo ad AB e pari alla sua metà.

Il quadrilatero MNQR è un parallelogramma avendo due lati opposti congruenti e paralleli e allora le sue diagonali NR e MQ si dividono scambievolmente per metà. In questo modo è dunque AQ=QG=GM e BR=RG=GN. Il che prova la prima parte della dimostrazione.

Se si ripete lo stesso ragionamento a partire dalle diagonali AM e CP, il loro punto di incontro G' le dividerà in due parti l'una doppia dell'altra. Ora poiché esiste un solo punto G che divide la mediana AM in modo che AG=2GM, il punto G' deve coincidere con G.

Portale Matematica: accedi alle voci di Wikipedia che trattano di matematica

Read other articles:

Denial of Peter

Episode from the Passion of Christ Peter's Denial redirects here. For other uses, see Peter's Denial (disambiguation). The Denial of Saint Peter, an oil-on-canvas painting by Gerard Seghers, dating to around 1620–25 and now held by the North Carolina Museum of Art[1] The Denial of Peter (or Peter's Denial) refers to three acts of denial of Jesus by the Apostle Peter as described in all four Gospels of the New Testament.[2] All four Canonical Gospels state that during Jesus's...

Metaescaline

Metaescaline Names Preferred IUPAC name 2-(3-Ethoxy-4,5-dimethoxyphenyl)ethan-1-amine Identifiers CAS Number 90132-31-3 Y 3D model (JSmol) Interactive image ChEMBL ChEMBL126963 Y ChemSpider 21106344 Y PubChem CID 44350068 UNII M4HNS35MM2 Y CompTox Dashboard (EPA) DTXSID30658376 InChI InChI=1S/C12H19NO3/c1-4-16-11-8-9(5-6-13)7-10(14-2)12(11)15-3/h7-8H,4-6,13H2,1-3H3 YKey: HNBAVLIQFTYMAX-UHFFFAOYSA-N YInChI=1/C12H19NO3/c1-4-16-11-8-9(5-6-13)7-10(14-2)12(11)15...

Battle of Bauds

Battle fought in 962 in Moray between Scotland and Norse pirates 57°38′56″N 2°53′35″W / 57.649°N 2.893°W / 57.649; -2.893 Battle of BaudsPart of the Viking invasions of ScotlandIndulf of Scotland, the famous Scottish king who fell during the Battle of BaudsDate962Locationnear Cullen, ScotlandResult Scottish victoryBelligerents Kingdom of Alba Kingdom of NorwayCommanders and leaders King Indulf † Unknown, possibly sons of Erik Bloodaxe[1] Battle of...

Antony, Hauts-de-Seine

Artikel ini perlu diterjemahkan dari bahasa Inggris ke bahasa Indonesia. Artikel ini ditulis atau diterjemahkan secara buruk dari Wikipedia bahasa Inggris. Jika halaman ini ditujukan untuk komunitas bahasa Inggris, halaman itu harus dikontribusikan ke Wikipedia bahasa Inggris. Lihat daftar bahasa Wikipedia. Artikel yang tidak diterjemahkan dapat dihapus secara cepat sesuai kriteria A2. Jika Anda ingin memeriksa artikel ini, Anda boleh menggunakan mesin penerjemah. Namun ingat, mohon tidak men...

Blåvandshuk

This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (March 2013) (Learn how and when to remove this template message) Blåvandshuk is a headland on the North Sea coast of Jutland northwest of Esbjerg, and is the westernmost point of metropolitan Denmark. The Blåvand Lighthouse is the westernmost located building in Denmark. Natural Environment A significant port...

2002 Minnesota Attorney General election

2002 Minnesota Attorney General election ← 1998 November 5, 2002 (2002-11-05) 2006 → Nominee Mike Hatch Thomas Kelly Party Democratic (DFL) Republican Popular vote 1,197,362 894,654 Percentage 54.6% 40.8% County results Precinct resultsHatch: 40–50% 50–60% 60–70% 70–80% 80–90% ...

2006 Polonskaya

2006 PolonskayaPenemuan[1]Ditemukan olehN. S. ChernykhTanggal penemuan22 September 1973PenamaanPenamaan alternatif Kategori planet minorSabuk utamaCiri-ciri orbit[2]Epos 4 Februari 2008 (JD 2454500.5)Aphelion415.038 Gm (2.774 SA)Perihelion280.622 Gm (1.876 SA)Sumbu semimayor347.830 Gm (2.325 SA)Eksentrisitas0.193Periode orbit1294.973 d (3.55 a)Kecepatan orbit rata-rata19.35 km/sAnomali rata-rata241.079°Inklinasi4.918°Bujur node menaik1.107°Ciri-ciri fisikDimensi10 kmMas...

Gempa bumi Irpinia 1980

Gempa bumi Irpinia 1980Kehancuran di CampaniaRomaWaktu UTC1980-11-23 18:34:52ISC635924USGS-ANSSComCatTanggal setempat23 November 1980 (23 November 1980)Waktu setempat19:34:52 CETKekuatan6.9 MwEpisentrum40°50′N 15°17′E / 40.84°N 15.28°E / 40.84; 15.28Koordinat: 40°50′N 15°17′E / 40.84°N 15.28°E / 40.84; 15.28Wilayah bencanaItaliaIntensitas maks.X (Ekstrem)Korban2,483 tewas 7,700–8,934 luka 250,000 mengungsi G...

Daftar Bupati Sumedang

Bupati Kabupaten Sumedang ᮊᮘᮥᮕᮒᮨᮔ᮪ ᮞᮥᮙᮨᮓᮀPetahanaDrs. H. Yudia Ramli, M.Si(Penjabat)sejak 20 April 2024KediamanPendopo Kabupaten SumedangMasa jabatan5 TahunDibentuk900Pejabat pertamaPrabu Guru Aji PutihSitus webwww.sumedang.go.id Berikut ini adalah artikel tentang daftar Bupati Sumedang dari mulai Kerajaan Sumedang Larang sampai Kabupaten Sumedang, provinsi Jawa Barat, Indonesia. # B u p a t i Mulai menjabat Akhir menjabat Wakil Bupati Catatan. Ref. 1 Nama Raj...

Falko Götz

Falko Götz Götz nel 2009 Nazionalità Germania Est Germania Ovest (dal 1984) Germania (dal 1990) Altezza 181 cm Calcio Ruolo Allenatore (ex centrocampista, attaccante) Termine carriera 1997 - giocatore CarrieraGiovanili 1969-1971 Vorwärts Berlino1971-1979 BFC DynamoSquadre di club1 1979-1983 BFC Dynamo40 (12)1984-1988 Bayer Leverkusen115 (26)1988-1992 Colonia127 (20)1992-1994 Galatasaray51 (16)1994-1995 Saarbrücken30 (5)1996-1997 Hertha ...

La Villedieu-du-Clain

La Villedieu-du-Claincomune La Villedieu-du-Clain – Veduta LocalizzazioneStato Francia Regione Nuova Aquitania Dipartimento Vienne ArrondissementPoitiers CantoneVivonne TerritorioCoordinate46°27′N 0°22′E / 46.45°N 0.366667°E46.45; 0.366667 (La Villedieu-du-Clain)Coordinate: 46°27′N 0°22′E / 46.45°N 0.366667°E46.45; 0.366667 (La Villedieu-du-Clain) Superficie7,17 km² Abitanti1 530[1] (2009) Densità213,39 ab...

马哈茂德·艾哈迈迪内贾德

馬哈茂德·艾哈迈迪-内贾德محمود احمدی‌نژاد第6任伊朗總統任期2005年8月3日—2013年8月3日副总统帷爾維茲·達烏迪穆罕默德-禮薩·拉希米领袖阿里·哈梅內伊前任穆罕默德·哈塔米继任哈桑·魯哈尼不结盟运动秘书长任期2012年8月30日—2013年8月3日前任穆罕默德·穆尔西继任哈桑·魯哈尼德黑蘭市長任期2003年6月20日—2005年8月3日副职阿里·賽義德盧前任哈桑·馬利克邁達尼�...

Società Sportiva Ponziana 1941-1942

Questa voce sull'argomento stagioni delle società calcistiche italiane è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Segui i suggerimenti del progetto di riferimento. Voce principale: Circolo Sportivo Ponziana 1912. Società Sportiva PonzianaStagione 1941-1942Sport calcio SquadraCircolo Sportivo Ponziana 1912 Allenatore Ferenc Plemich Presidente Amleto Starace Serie C6º posto nel girone eliminatorio A 1940-1941 1942-1943 Si invita a seguire il mod...

قائمة البطاركة الموارنة

بطريرك أنطاكية وسائر المشرق للكنيسة المارونية بكركي، لبنان قائمة البطاركة الموارنةشعار البطريركية المارونية شاغل المنصب بشارة بطرس الراعي منذ 15 آذار 2011 عن المنصب المعين المجمع المقدّس للكنيسة المارونية تأسيس المنصب أواخر القرن السابع أول حامل للمنصب القديس يوحنا م�...

Mike Braun

American businessman and politician (born 1954) For other people with similar names, see Michael Braun (disambiguation). Mike BraunOfficial portrait, 2019United States Senatorfrom IndianaIncumbentAssumed office January 3, 2019Serving with Todd YoungPreceded byJoe DonnellyRanking Member of the Senate Aging CommitteeIncumbentAssumed office January 3, 2023Preceded byTim ScottMember of the Indiana House of Representativesfrom the 63rd districtIn officeNovember 5, 2014&...

Mahoning County, Ohio

County in Ohio, United States County in OhioMahoning CountyCountyMahoning County Courthouse FlagSealLocation within the U.S. state of OhioOhio's location within the U.S.Coordinates: 41°01′N 80°46′W / 41.02°N 80.77°W / 41.02; -80.77Country United StatesState OhioFoundedMarch 1, 1846Named forA Native American word for salt lickSeatYoungstownLargest cityYoungstownArea • Total425 sq mi (1,100 km2) • Land412 sq&#...

Universitas Khon Kaen

Universitas Khon Kaenมหาวิทยาลัยขอนแก่นMotoวิทยา จริยา ปัญญาJenisUniversitas negeriDidirikan1966[1]PresidenChanchai PhanthongweerayakulStaf administrasi2,075[2] (2007)Jumlah mahasiswa37,605[3] (2020)LokasiDistrik Mueang Khon Kaen, Khon Kaen, Thailand16°28′13″N 102°48′57″E / 16.470329°N 102.815927°E / 16.470329; 102.815927Koordinat: 16°28′13″N 102°48′57″Eþ...

赵晓哲

此條目需要擴充。 (2012年3月4日)请協助改善这篇條目，更進一步的信息可能會在討論頁或扩充请求中找到。请在擴充條目後將此模板移除。赵晓哲（1963年7月7日—），男，辽宁大连人，中国人民解放军海军大连舰艇学院教授、博士生导师，海军中将，中央军事委员会科学技术委员会主任，中国工程院院士。[1] 生平赵晓哲曾在大连理工大学计算机科学与工程系学习，获...

Kim Se-jeong

Ini adalah nama Korea; marganya adalah Kim. Kim Se-jeongSejeong pada 2022.Nama asal김세정LahirKim Se-jeong28 Agustus 1996 (umur 27)Gimje, Jeolla Utara[1]PendidikanHanyang Women's UniversityPekerjaanPenyanyiPemeranTinggi164 cm (5 ft 5 in)Berat89 kg (196 pon)Karier musikGenreK-pop, Musik baladaTahun aktif2016–presentLabelJellyfish Entertainment (2016–present)YMC Entertainment (2016–2017)Artis terkaitI.O.IGugudanNama KoreaHangul김세정 Hanja�...

Arie Soedewo

Arie Soedewo Kepala Badan Keamanan Laut 7Masa jabatan16 Maret 2016 – 24 September 2018PendahuluLaksdya TNI Desi Albert MamahitPenggantiLaksdya TNI Achmad TaufiqoerrochmanAsisten Operasi KASALMasa jabatan2015–2016PendahuluLaksda TNI Arie Henrycus SembiringPenggantiLaksda TNI INGN Ary AtmajaKoordinator Staf Ahli KASALMasa jabatan30 Maret 2015 – 18 Agustus 2015PendahuluAchmad TaufiqoerrochmanPenggantiDidik Wahyudi Informasi pribadiLahir1 Mei 1960 (umur 64)Banjar,...