[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.72,0:00:02.55,Default,,0000,0000,0000,,Deci, avem un parallelogram chiar aici
Dialogue: 0,0:00:02.56,0:00:06.66,Default,,0000,0000,0000,,Ce vrem sa aratam este ca diagonalele lui se \Nimpart in parti egale
Dialogue: 0,0:00:06.67,0:00:10.04,Default,,0000,0000,0000,,Deci, primul lucru la care ne gandim, acestea nu sunt\Nnumai diagonale
Dialogue: 0,0:00:10.05,0:00:12.46,Default,,0000,0000,0000,,acestea sunt linii care interesecteaza linii\Nparalele
Dialogue: 0,0:00:12.47,0:00:14.56,Default,,0000,0000,0000,,Deci, le putem vedea precum transversale
Dialogue: 0,0:00:14.57,0:00:19.54,Default,,0000,0000,0000,,Si daca ne focusam la DB chiar aici, vedem ca \Nintersecteaza DC
Dialogue: 0,0:00:19.55,0:00:21.89,Default,,0000,0000,0000,,si AB si sta acolo
Dialogue: 0,0:00:21.90,0:00:23.64,Default,,0000,0000,0000,,Acelea stim ca sunt paralelograme
Dialogue: 0,0:00:23.65,0:00:24.96,Default,,0000,0000,0000,,Stim ca ele sunt paralele
Dialogue: 0,0:00:24.97,0:00:25.99,Default,,0000,0000,0000,,Acesta este un paralelogram
Dialogue: 0,0:00:26.00,0:00:28.64,Default,,0000,0000,0000,,Unghiurile alterne interne trebuie sa fie congruente
Dialogue: 0,0:00:28.65,0:00:31.36,Default,,0000,0000,0000,,Deci, acel unghi teebuie sa fie egal cu acel unghi \Nde acolo
Dialogue: 0,0:00:31.37,0:00:32.67,Default,,0000,0000,0000,,Hai sa marchez aici
Dialogue: 0,0:00:32.68,0:00:34.03,Default,,0000,0000,0000,,Hai sa numesc punctul din mijloc E
Dialogue: 0,0:00:34.04,0:00:42.63,Default,,0000,0000,0000,,Deci, stim ca unghiul ABE trebuie sa fie congruent cu\Nunghiul CDE
Dialogue: 0,0:00:42.64,0:00:50.13,Default,,0000,0000,0000,,ca unghiuri alterne interne
Dialogue: 0,0:00:50.14,0:00:52.13,Default,,0000,0000,0000,,o transversala taie liniile paralele
Dialogue: 0,0:00:52.14,0:00:56.68,Default,,0000,0000,0000,,Unghiurile alterne interne
Dialogue: 0,0:00:56.69,0:01:00.84,Default,,0000,0000,0000,,Daca ne uitam la diagonala AC sau o vom numi \Ntransversala AC
Dialogue: 0,0:01:00.85,0:01:02.52,Default,,0000,0000,0000,,putem face aceelasi argument
Dialogue: 0,0:01:02.73,0:01:04.47,Default,,0000,0000,0000,,Intersecteaza aici si aici
Dialogue: 0,0:01:04.48,0:01:06.22,Default,,0000,0000,0000,,Aceste doua linii sunt paralele
Dialogue: 0,0:01:06.23,0:01:09.36,Default,,0000,0000,0000,,Deci, unghiurile alterne interne sunt congruente
Dialogue: 0,0:01:09.37,0:01:12.74,Default,,0000,0000,0000,,Deci, unghiul DEC trebuie sa fie-- hai sa scriu --
Dialogue: 0,0:01:12.75,0:01:19.05,Default,,0000,0000,0000,,unghiul DEC trebuie sa fie congruent cu unghiul BAE
Dialogue: 0,0:01:24.78,0:01:27.15,Default,,0000,0000,0000,,din aceelasi motiv
Dialogue: 0,0:01:27.16,0:01:28.68,Default,,0000,0000,0000,,Acum avem ceva interesant
Dialogue: 0,0:01:28.69,0:01:31.58,Default,,0000,0000,0000,,Daca ne uitam la acest triunghi de sus si acest\Ntriunghi de jos,
Dialogue: 0,0:01:31.59,0:01:34.82,Default,,0000,0000,0000,,avem un set de unghiuri corespondente care sunt\Ncongruente
Dialogue: 0,0:01:34.83,0:01:39.61,Default,,0000,0000,0000,,Avem o latura intre ele care va fi congruenta
Dialogue: 0,0:01:39.62,0:01:41.22,Default,,0000,0000,0000,,De fapt, hai sa scriu asta explicit
Dialogue: 0,0:01:41.23,0:01:46.38,Default,,0000,0000,0000,,Stim si am demonstrat in video-ul dinainte
Dialogue: 0,0:01:46.67,0:01:50.38,Default,,0000,0000,0000,,ca in paralelograme nu numai laturile opuse sunt \Nparalele , ele sunt
Dialogue: 0,0:01:50.39,0:01:51.54,Default,,0000,0000,0000,,si congruente
Dialogue: 0,0:01:51.55,0:01:54.31,Default,,0000,0000,0000,,Deci, stim din video-ul anterior ca acea latura e egala
Dialogue: 0,0:01:54.32,0:01:55.23,Default,,0000,0000,0000,,cu acea latura
Dialogue: 0,0:01:55.24,0:01:56.84,Default,,0000,0000,0000,,Deci, hai sa merg inapoi la ceea ce spuneam
Dialogue: 0,0:01:56.85,0:01:59.76,Default,,0000,0000,0000,,Avem doua seturi de unghiuri corespondente care\Nsunt conguente
Dialogue: 0,0:01:59.77,0:02:02.71,Default,,0000,0000,0000,,Avem o latura intre care este congruenta
Dialogue: 0,0:02:02.72,0:02:04.74,Default,,0000,0000,0000,,Si apoi avem un alt set de unghiuri corespondente
Dialogue: 0,0:02:04.75,0:02:05.77,Default,,0000,0000,0000,,care sunt congruente
Dialogue: 0,0:02:05.78,0:02:08.15,Default,,0000,0000,0000,,Deci, stim ca acest triunghi e congruent cu acel \Ntriunghi
Dialogue: 0,0:02:08.16,0:02:10.32,Default,,0000,0000,0000,,cu cazul unghi-latura-unghi
Dialogue: 0,0:02:11.81,0:02:15.96,Default,,0000,0000,0000,,Deci, stim ca triunghiul -- voi merge de la albastru
Dialogue: 0,0:02:15.97,0:02:17.46,Default,,0000,0000,0000,,la portocaliu pentru ultima data
Dialogue: 0,0:02:17.47,0:02:23.12,Default,,0000,0000,0000,,Triunghiul ABE e congruent cu triunghiul albastru,\Nportocaliu
Dialogue: 0,0:02:23.13,0:02:29.97,Default,,0000,0000,0000,,si ultimul, CDE cu cazul de congruenta \Nunghi - latura- unghi
Dialogue: 0,0:02:33.72,0:02:35.94,Default,,0000,0000,0000,,Acum ce face asta pentru noi
Dialogue: 0,0:02:35.95,0:02:38.86,Default,,0000,0000,0000,,Ce stim daca doua triunghiuri sunt congruente,\Ntoate
Dialogue: 0,0:02:38.87,0:02:41.37,Default,,0000,0000,0000,,caracteristicile lor corespunzatoare, in mod special \Ntoate
Dialogue: 0,0:02:41.38,0:02:42.62,Default,,0000,0000,0000,,laturile coresunzatoare sunt congruente
Dialogue: 0,0:02:42.63,0:02:47.74,Default,,0000,0000,0000,,Deci, stim ca latura EC corespunde la EA
Dialogue: 0,0:02:47.75,0:02:51.92,Default,,0000,0000,0000,,Sau as putea spune latura AE, putem spune latura AE,
Dialogue: 0,0:02:55.24,0:02:59.47,Default,,0000,0000,0000,,corespunde laturii CE
Dialogue: 0,0:03:00.99,0:03:02.83,Default,,0000,0000,0000,,Ele sunt laturi coresounzatoare in triunghiuri congruente
Dialogue: 0,0:03:02.84,0:03:05.36,Default,,0000,0000,0000,,Deci, masura lor sau lungimile lor trebuie sa fie la fel
Dialogue: 0,0:03:05.37,0:03:08.85,Default,,0000,0000,0000,,Deci, AE trebuie sa fie egala cu CE
Dialogue: 0,0:03:08.86,0:03:12.32,Default,,0000,0000,0000,,Hai sa pun doua liniute mai ales ca am folosit o liniuta\Naici
Dialogue: 0,0:03:18.21,0:03:24.32,Default,,0000,0000,0000,,hai sa ma focusez pe asta-- stim ca BE trebuie \Nsa fie egal cu DE
Dialogue: 0,0:03:25.95,0:03:29.45,Default,,0000,0000,0000,,Din noi sunt laturi corespundente in doua triunghiuri\Ncongruente
Dialogue: 0,0:03:29.46,0:03:30.87,Default,,0000,0000,0000,,deci trebuie sa aiba aceeasi lungime
Dialogue: 0,0:03:30.88,0:03:38.32,Default,,0000,0000,0000,,Deci, acestea sunt laturi corespondente in triunghiuri\Ncongruente
Dialogue: 0,0:03:38.33,0:03:43.00,Default,,0000,0000,0000,,Deci, BE e egal cu DE
Dialogue: 0,0:03:43.01,0:03:44.08,Default,,0000,0000,0000,,Si am demonstrat
Dialogue: 0,0:03:44.09,0:03:48.78,Default,,0000,0000,0000,,Am aratat ca, uitati, diagonala DB imparte AC in doua
Dialogue: 0,0:03:48.79,0:03:51.23,Default,,0000,0000,0000,,segmente de lungime egala si vice versa
Dialogue: 0,0:03:51.24,0:03:55.78,Default,,0000,0000,0000,,AC imparte DB in doua segmente de lungime egala
Dialogue: 0,0:03:55.79,0:03:58.07,Default,,0000,0000,0000,,Deci, ele se impart in parti egale
Dialogue: 0,0:03:58.08,0:03:59.64,Default,,0000,0000,0000,,Acum, hai sa merg invers
Dialogue: 0,0:03:59.65,0:04:03.92,Default,,0000,0000,0000,,Hai sa demonstram ca daca avem doua diagonale
Dialogue: 0,0:04:03.93,0:04:06.98,Default,,0000,0000,0000,,ale unui patrulater care se taie in parti egale
Dialogue: 0,0:04:06.99,0:04:08.81,Default,,0000,0000,0000,,avem de a face cu un paralelogram
Dialogue: 0,0:04:08.82,0:04:10.02,Default,,0000,0000,0000,,Deci, hai sa vad
Dialogue: 0,0:04:10.03,0:04:12.01,Default,,0000,0000,0000,,Deci, vom asuma ca cele doua diagonale
Dialogue: 0,0:04:12.02,0:04:13.15,Default,,0000,0000,0000,,se taie in parti egale
Dialogue: 0,0:04:13.16,0:04:14.98,Default,,0000,0000,0000,,Deci, asumam ca aceasta este egala cu aceasta
Dialogue: 0,0:04:14.99,0:04:17.36,Default,,0000,0000,0000,,Si ca aceasta, de aici, e egala cu aceasta
Dialogue: 0,0:04:17.37,0:04:22.29,Default,,0000,0000,0000,,Dat fiind asta, vrem sa demonstram ca acesta este\Nparalelogram
Dialogue: 0,0:04:22.30,0:04:25.16,Default,,0000,0000,0000,,Si ca sa facem asta trebuie sa ne reamintim
Dialogue: 0,0:04:25.44,0:04:30.00,Default,,0000,0000,0000,,Trebuie sa ne reamintim ca acest unghi
Dialogue: 0,0:04:30.01,0:04:31.04,Default,,0000,0000,0000,,va fi egal cu acel unghi
Dialogue: 0,0:04:31.05,0:04:33.73,Default,,0000,0000,0000,,Unul dintre primele lucruri am invatat deoarece\Nsunt unghiuri drepte
Dialogue: 0,0:04:33.74,0:04:34.64,Default,,0000,0000,0000,,Deci, hai sa scriu
Dialogue: 0,0:04:34.65,0:04:43.58,Default,,0000,0000,0000,,C -- am notat acest punct -- unghiul CED va fi egal cu
Dialogue: 0,0:04:43.59,0:04:52.39,Default,,0000,0000,0000,,sau va fi congruent cu unghiul, deci am inceput\Neste BEA, unghiul BEA
Dialogue: 0,0:04:52.40,0:04:55.20,Default,,0000,0000,0000,,Si aceasta, ce este aceasta, ei bine ne arata ca aceste
Dialogue: 0,0:04:55.21,0:04:57.81,Default,,0000,0000,0000,,doua triunghiuri sunt congruente deoarece avem \Nlaturi corespunzatoare
Dialogue: 0,0:04:57.82,0:05:00.31,Default,,0000,0000,0000,,si unghiuri congrunete intre ele pe de alta parte
Dialogue: 0,0:05:00.32,0:05:03.81,Default,,0000,0000,0000,,Deci, acum stim ca triunghiul, il tin in galben,
Dialogue: 0,0:05:03.82,0:05:20.30,Default,,0000,0000,0000,,triunghiul AEB e congruent cu triunghiul DEC cu\Ncazul latura-unghi-latura
Dialogue: 0,0:05:20.31,0:05:28.17,Default,,0000,0000,0000,,cu cazul de congruenta al triunghiurilor LUL
Dialogue: 0,0:05:28.18,0:05:29.16,Default,,0000,0000,0000,,Corect
Dialogue: 0,0:05:29.17,0:05:31.76,Default,,0000,0000,0000,,Acum, daca stim ca doua triunghiuri sunt congruente\Nstim ca toate
Dialogue: 0,0:05:31.77,0:05:34.22,Default,,0000,0000,0000,,laturile coresunzatoare si unghuiri sunt congruente
Dialogue: 0,0:05:34.23,0:05:44.58,Default,,0000,0000,0000,,Deci, de exemplu, stim ca unghiul CED va fi congruent
Dialogue: 0,0:05:44.59,0:05:48.36,Default,,0000,0000,0000,,cu unghiul BAE
Dialogue: 0,0:05:55.65,0:06:05.79,Default,,0000,0000,0000,,Si asta este doar unghiuri coresponente in \Ntriunghiuri congruente
Dialogue: 0,0:06:05.80,0:06:12.43,Default,,0000,0000,0000,,Si acum avem acet tip de transversala a acestor doua linii
Dialogue: 0,0:06:12.44,0:06:16.57,Default,,0000,0000,0000,,care pot fi paralele daca unghiurile alterne interne sunt \Ncongruente
Dialogue: 0,0:06:16.58,0:06:17.99,Default,,0000,0000,0000,,Si vedem ca sunt
Dialogue: 0,0:06:18.00,0:06:22.47,Default,,0000,0000,0000,,Acestea doua sunt cam candidate la unghiuri\Nalterne interne si
Dialogue: 0,0:06:22.48,0:06:23.91,Default,,0000,0000,0000,,ele sunt congruente
Dialogue: 0,0:06:23.92,0:06:26.87,Default,,0000,0000,0000,,Deci, AB trebuie sa fie parallel cu CD
Dialogue: 0,0:06:26.88,0:06:31.78,Default,,0000,0000,0000,,Deci, AB , hai sa desenam o sageata,\NAB trebuie sa fie paralela cu CD
Dialogue: 0,0:06:34.95,0:06:42.62,Default,,0000,0000,0000,,deoarece unghiurile alterne interne sunt congruente \Na liniilor paralele
Dialogue: 0,0:06:42.80,0:06:46.11,Default,,0000,0000,0000,,O scriu in forma presurtata, scuzati natura criptica
Dialogue: 0,0:06:46.12,0:06:47.67,Default,,0000,0000,0000,,desi o zic tare
Dialogue: 0,0:06:47.68,0:06:50.30,Default,,0000,0000,0000,,Si apoi putem face exact aceelasi lucru--\Nin timp ce doar am aratat
Dialogue: 0,0:06:50.31,0:06:53.23,Default,,0000,0000,0000,,ca aceste doua linii sunt paralele - \Nputem face aceelasi lucru
Dialogue: 0,0:06:53.24,0:06:55.64,Default,,0000,0000,0000,,logic sa aratam ca aceste doua laturi sunt paralele
Dialogue: 0,0:06:55.65,0:06:57.09,Default,,0000,0000,0000,,Nu neaparat scriu totul
Dialogue: 0,0:06:57.10,0:06:59.97,Default,,0000,0000,0000,,Este exact aceeasi demonstratie sa aratam aceste doua
Dialogue: 0,0:06:59.98,0:07:03.68,Default,,0000,0000,0000,,Deci, mai intai, stim ca acest unghi e congruent cu\Nacel unghi
Dialogue: 0,0:07:03.69,0:07:04.63,Default,,0000,0000,0000,,de acolo
Dialogue: 0,0:07:04.64,0:07:06.93,Default,,0000,0000,0000,,Si apoi stim, hai sa o scriu, stim
Dialogue: 0,0:07:06.94,0:07:18.67,Default,,0000,0000,0000,,ca unghiul AEC e congruent cu unghiul DEB, \Nas putea spune
Dialogue: 0,0:07:22.65,0:07:24.36,Default,,0000,0000,0000,,Sunt unghiuri verticale
Dialogue: 0,0:07:26.98,0:07:29.06,Default,,0000,0000,0000,,Si asta e motivul aici sus de asemeni
Dialogue: 0,0:07:29.07,0:07:31.92,Default,,0000,0000,0000,,Unghiuri verticale
Dialogue: 0,0:07:31.93,0:07:35.26,Default,,0000,0000,0000,,Si apoi vedem ca triunghiul AEC trebuie sa fie \Ncongruent
Dialogue: 0,0:07:35.27,0:07:38.27,Default,,0000,0000,0000,,cu triunghiul DEB cu latura-unghi- latura
Dialogue: 0,0:07:38.60,0:07:45.01,Default,,0000,0000,0000,,Deci, apoi avem triunghiul AEC trebuie sa fie congruent\Ncu triunghiul
Dialogue: 0,0:07:45.02,0:07:50.89,Default,,0000,0000,0000,,DEB cu cazul de congruenta LUL
Dialogue: 0,0:07:50.90,0:07:53.73,Default,,0000,0000,0000,,Acum, stim ca unghiurile corespunzatoare trebuie \Nsa fie congruente
Dialogue: 0,0:07:53.74,0:07:58.68,Default,,0000,0000,0000,,Deci, ca stim ca acel unghi, deci, de exemplu \Nunghiul CAE
Dialogue: 0,0:08:01.76,0:08:10.97,Default,,0000,0000,0000,,treubie sa fie congruent cu unghiul BDE si acestea sunt
Dialogue: 0,0:08:10.98,0:08:13.51,Default,,0000,0000,0000,,unghiurile coresunzatoare ale triunghiurilor congruente
Dialogue: 0,0:08:13.52,0:08:17.95,Default,,0000,0000,0000,,Deci, CAE, hai sa folosesc o culoare noua
Dialogue: 0,0:08:18.13,0:08:25.94,Default,,0000,0000,0000,,CAE trebuie sa fie congruent cu BDE
Dialogue: 0,0:08:28.05,0:08:30.10,Default,,0000,0000,0000,,Si acum avem o transversala
Dialogue: 0,0:08:30.11,0:08:32.10,Default,,0000,0000,0000,,Unghiurile alterne interne sunt congruente
Dialogue: 0,0:08:32.11,0:08:34.69,Default,,0000,0000,0000,,Deci, cele doua linii pe care le taie transversala
Dialogue: 0,0:08:34.70,0:08:36.13,Default,,0000,0000,0000,,trebuie sa fie paralele
Dialogue: 0,0:08:36.14,0:08:39.23,Default,,0000,0000,0000,,Deci, aceasta trebuie sa fie paralela cu aceasta
Dialogue: 0,0:08:39.24,0:08:44.44,Default,,0000,0000,0000,,Deci, apoi avem AC trebuie sa fie paralela cu BD
Dialogue: 0,0:08:45.49,0:08:47.97,Default,,0000,0000,0000,,cu unghuri alterne interne
Dialogue: 0,0:08:50.56,0:08:51.36,Default,,0000,0000,0000,,Si am terminat
Dialogue: 0,0:08:51.37,0:08:53.97,Default,,0000,0000,0000,,Tocmai am dovedit ca daca diagonalele se taie in\Nparti egale,
Dialogue: 0,0:08:53.98,0:08:57.91,Default,,0000,0000,0000,,daca am inceput ca fiind ceva dat am sfarsit \Nla un punct unde spunem,
Dialogue: 0,0:08:57.92,0:09:00.86,Default,,0000,0000,0000,,"Hei, laturile opuse ale acestui patrulater trebuie \Nsa fie paralele
Dialogue: 0,0:09:00.87,0:09:04.69,Default,,0000,0000,0000,,sau acest ABCD este parallelogram"