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Clár

Select the proof required then click mouse key to view proof. Clár. Teoirim 4 Suimíonn an 3 uillinn I dtriantán suas go 180 céim. Teoirim 6 Tá an uillinn seachtrach I dtriantán cothrom le suim an dá uillinn urchomhaireacht inmheánach.

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Clár

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  1. Select the proof required then click mouse key to view proof. Clár Teoirim 4 Suimíonn an 3 uillinn I dtriantánsuas go 180 céim. Teoirim 6 Tá an uillinnseachtrach I dtriantáncothrom le suim an dáuillinnurchomhaireachtinmheánach. Theorem 9 Tásleasaurchomhaireachaagusuillnneachaurchomaireacha I gcomhthreomharánarcomhéid (agus a mhalairt ) Teoirim14 I dtriantándronuilleachtá fad an tsleasaoscomhairnadronuillinnecothrom le suimfhadcearnaithe an dáshlioseile. (Pythagorais) Teoirim 19 Tátomhasnahullinneaglárciorcailcothrom le dháoiread thomhasnauillinneag an imlíneagseasamhar an stualcéanna Constructions Sketches Quit

  2. 4 5 3 1 2 Teoirim 4:Suimíonn an 3 uillinnidtriantánsuas go 1800 . Use mouse clicks to see proof Tugtha:Triantán CruthúÐ3 + Ð4 + Ð5 = 1800Line Direach Ð1 = Ð4 agusÐ2 = Ð5 Ailtéarnach ÞÐ3 + Ð1 + Ð2 = 1800 Ð1 + Ð2 + Ð3 = 1800 Q.E.D. Le Cruthú:Ð1 + Ð2 + Ð3 = 1800 Tógáil:TarrainglínetríÐ3 comhthreomhar leis an mbonn Constructions Sketches Menu Quit

  3. 90 45 135 3 0 180 1 2 4 Teoirim6:Tá an uillinnsheachtrachidtriantáncothrom le suim an dáuillinnurchomhaireachinmheánach. Use mouse clicks to see proof Le Cruthú:Ð1 = Ð3 + Ð4 Cruthú:Ð1 + Ð2 = 1800 …………..LíneDíreach Ð2 + Ð3 + Ð4 = 1800 ………….. Teoirim 2 (3 uillinni ∆ = 1800). Þ Ð1 + Ð2 = Ð2 + Ð3 + Ð4 Þ Ð1 = Ð3 + Ð4 Q.E.D. Constructions Sketches Menu Quit

  4. B C A D Teoirim 9: I gComhthreomharán, tánasleasaurchomhaireachaagusnahuillinneachaurchomhaireacha,, faoiseach, cothromlenachéile. Use mouse clicks to see proof Tugtha:Comhthreomharán ABCD Le Cruthú:|AB| = |CD| agus|AD| = |BC| agusÐABC = ÐADC 3 4 TógáílTarraing an trasnán |AC| 1 Cruthú:Sa triantán ABC agussatriantán ADC 2 Ð1 = Ð4 …….. Ailtéarnach Ð2 = Ð3 ……… Ailtéarnach |AC| = |AC| …… Comónta Þ Tá an triantán ABC comhionann leis an triantán ADC……… USU = USU. Þ|AB| = |CD| agus |AD| = |BC| agusÐABC = ÐADC Q.E.D Constructions Sketches Menu Quit

  5. b a a c b c c c a b b a Teoirim 14 I dtriantándronuilleachtá fad an tsleasaoscomhairnadronuillinnecothrom le suimfhadcearnaithe an dáshlioseile. Úsáid do luch chun cliceáil Tugtha : An Triantánabc Le Cruthú:a2 + b2 = c2 Tógáil3 Thriantándronuilleach mar léirithe Cruthú:Acharna móire. = acharna bige + 4(acharD) (a + b)2 = c2 + 4(½ab) a2 + 2ab +b2 = c2 + 2ab a2 + b2 = c2 Q.E.D. Constructions Sketches Menu Quit

  6. A O R C B Teoirim19:Tátomhasnahullinneaglárciorcailcothrom le dháoiread thomhasnauillinneag an imlíneagseasamhar an stualcéanna . Dein cliceáil ar do luch chun gach céim a fheiscint Le Cruthú:| ÐBOC| = 2 | ÐBAC | 5 2 Tógáil:CeangailA le O agussínigh é amach go R Cruthú: Sa triantánAOB 4 1 3 | OA| = | OB | …… Is gathannaiadaraon Þ | Ð2 | = | Ð3 | …… Triantáncomhchosach | Ð1 | = | Ð2 | + | Ð3 | …… Uillinnsheachtrach Þ | Ð1 | = | Ð2 | + | Ð2 | Þ | Ð1 | = 2| Ð2 | Mar an gcéannasatriantáneile | Ð4 | = 2| Ð5 | Q.E.D Þ | ÐBOC | = 2 | ÐBAC | Constructions Sketches Menu Quit

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