{"id":2383,"date":"2021-04-27T09:19:15","date_gmt":"2021-04-27T09:19:15","guid":{"rendered":"http:\/\/accesis.ro\/blog\/?p=2383"},"modified":"2022-02-18T10:44:54","modified_gmt":"2022-02-18T10:44:54","slug":"aria-triunghiului-isoscel","status":"publish","type":"post","link":"https:\/\/accesis.ro\/blog\/aria-triunghiului-isoscel\/","title":{"rendered":"Aria triunghiului isoscel | Meticulos, simplificat, explica\u021bii vizuale"},"content":{"rendered":"\n<p class=\"has-vivid-cyan-blue-color has-text-color has-medium-font-size\" id=\"aria-triunghi-isoscel\"><strong><a href=\"https:\/\/accesis.lpages.co\/meditatii-matematica-romana\/\" target=\"_blank\" rel=\"noreferrer noopener\">Inva\u021b\u0103 matematic\u0103 online, cu profesor. Meticulos, simplificat, explica\u021bii vizuale.<\/a> <span style=\"color:#0f64b9\" class=\"has-inline-color\"><a href=\"https:\/\/accesis.lpages.co\/meditatii-matematica-romana\/\" target=\"_blank\" rel=\"noreferrer noopener\">Intr\u0103 pe site<\/a><\/span><span style=\"color:#0f60b3\" class=\"has-inline-color\"> <\/span>sau \u00eentreaba-ne detalii: office@accesis.ro<\/strong><\/p>\n\n\n\n<p><strong>Triunghiul isoscel are prin definitie doua laturi congruente si o baza.<\/strong> Unghiurile si liniile importante sunt: mediana, mediatoare, bisectoare \u0219i \u00een\u0103l\u021bime. Calculul Ariei <\/p>\n\n\n\n<p><strong>Teorema:<\/strong> intr-un triunghi isoscel, unghiurile alaturate bazei sunt congruente. <\/p>\n\n\n\n<p><strong>Reciproca teoremei:<\/strong> daca un triunghi are doar doua unghiuri congruente atunci el este isoscel. <\/p>\n\n\n\n<p>Intr-un triunghi isoscel mediana corespunzatoare bazei este <span class=\"has-inline-color has-vivid-red-color\"><strong>si <\/strong>mediatoare <strong>si<\/strong> bisectoare <strong>si<\/strong> inaltime<\/span>. <strong>OBS:<\/strong> Daca o linie importanta este mediatoare, este suficienta pentru ca triunghiul sa fie isoscel. Asta pentru ca mediatoarea trece prin mijlocul segmentului <span class=\"has-inline-color has-vivid-red-color\">(este mediana)<\/span> si este perpendiculara pe segment <span class=\"has-inline-color has-vivid-red-color\">(este inaltime)<\/span><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"512\" height=\"405\" src=\"http:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/triunghi-isoscel.jpg\" alt=\"\" class=\"wp-image-2384\" srcset=\"https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/triunghi-isoscel.jpg 512w, https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/triunghi-isoscel-300x237.jpg 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/figure><\/div>\n\n\n\n<p><\/p>\n\n\n\n<p>Prin cobor\u00eerea \u00een\u0103l\u0163imii, \u00een triunghiul isoscel cu catetele egale se formeaz\u0103 <strong>dou\u0103 triunghiuri dreptunghice<\/strong> <em>(au c\u00e2te un unghi drept, de 90 grade)<\/em> perfect egale. ( laturi, unghiuri \u015fi arii) \u00cen triunghiul dreptunghic fiecare catet\u0103 este egal\u0103 cu media geometric\u0103 dintre ipotenuz\u0103 \u0219i proiec\u021bia catetei pe ipotenuz\u0103.<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-red-color\">Pentru a afla aria unui triunghi isoscel vom calcula intai aria unuia dintre triunghiurile dreptunghice formate prin cobor\u00eerea \u00een\u0103l\u0163imii.<\/span><\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"http:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/arie-triunghi-isoscel-2-1024x523.png\" alt=\"\" class=\"wp-image-2391\" width=\"669\" height=\"341\" srcset=\"https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/arie-triunghi-isoscel-2-1024x523.png 1024w, https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/arie-triunghi-isoscel-2-300x153.png 300w, https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/arie-triunghi-isoscel-2-768x392.png 768w, https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/arie-triunghi-isoscel-2.png 1096w\" sizes=\"(max-width: 669px) 100vw, 669px\" \/><\/figure><\/div>\n\n\n\n<p class=\"has-text-align-center\"><strong><span style=\"color:#0d6598\" class=\"has-inline-color\"><a href=\"https:\/\/accesis.lpages.co\/meditatii-matematica-romana\/\" target=\"_blank\" rel=\"noreferrer noopener\">Pregateste-te la matematica cu profesor online<\/a>. <\/span><span class=\"has-inline-color has-vivid-red-color\"><a href=\"https:\/\/accesis.lpages.co\/meditatii-matematica-romana\/\" target=\"_blank\" rel=\"noreferrer noopener\">Intra pe pagin<\/a><\/span><\/strong><span class=\"has-inline-color has-vivid-red-color\"><a rel=\"noreferrer noopener\" href=\"https:\/\/accesis.lpages.co\/meditatii-bucuresti\/\" target=\"_blank\">a <\/a><\/span><\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-red-color\">\u00centr-un triunghi dreptunghic<\/span><\/strong> <em>(triunghiul care are un unghi drept, de 90 grade)<\/em> lungimea \u00een\u0103l\u021bimii corespunz\u0103toare ipotenuzei <em>(ipotenuza = latura opusa unghiului de 90 de grade)<\/em> este egal\u0103 cu media geometric\u0103 a lungimilor proiec\u021biilor catetelor (celelalte 2 laturi) pe ipotenuz\u0103. <\/p>\n\n\n\n<p class=\"has-text-align-left\"><strong>Lungimea \u00een\u0103l\u021bimii in triunghiul dreptunghic se calculeaza astfel <\/strong>= \u221a(x \u00b7 4x) = \u221a(4x\u00b2) = 2x<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-red-color\">Aria \u00eentr-un triunghi dreptunghic&nbsp;<\/span><\/strong>este egal\u0103 cu semiprodusul catetelor sau semiprodusul dintre ipotenuza si inaltime. <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" loading=\"lazy\" width=\"442\" height=\"372\" src=\"http:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/Formula-arie-triunghi-isoscel.png\" alt=\"\" class=\"wp-image-2390\" srcset=\"https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/Formula-arie-triunghi-isoscel.png 442w, https:\/\/accesis.ro\/blog\/wp-content\/uploads\/2021\/04\/Formula-arie-triunghi-isoscel-300x252.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/figure>\n\n\n\n<p><strong>Aplicarea Teoremei Lui Pitagora La Triunghiul Isoscel<\/strong><\/p>\n\n\n\n<p><a href=\"https:\/\/ro.wikipedia.org\/wiki\/Teorema_lui_Pitagora\">Teorema lui Pitagora<\/a>: \u201e<em>suma p\u0103tratelor lungimilor catetelor este egal\u0103 cu p\u0103tratul lungimii ipotenuzei<\/em>\u201d. Aceasta poate fi reprezentat\u0103 \u00een triunghiul dreptunghic ABC, AB fiind ipotenuza, iar C unghiul drept. <\/p>\n\n\n\n<p>Teorema lui Pitagora spune c\u0103: <img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/d6c537ddf3156d95f60b5425cc97e2f8c6b30961\" alt=\"{\\displaystyle AB^{2}=AC^{2}+BC^{2}}\"><\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-red-color\">Pentru un triunghi isoscel oarecare <\/span><\/strong><em><span class=\"has-inline-color has-black-color\">(cu unghiul dintre catete diferit de 90)<\/span><\/em><strong><span class=\"has-inline-color has-vivid-red-color\"> pentru calcularea ariei putem folosi doar Teorema lui Pitagora<\/span><\/strong>. Prin teorema lui Pitagora afl\u0103m dimensiunea \u00een\u0103l\u0163imii. Apoi aplic\u0103m formula ariei triunghiului, <strong>b x h \/ 2<\/strong> (baza ori \u00een\u0103l\u0163imea supra 2).&nbsp;<\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><strong>Teorema catetei <\/strong><\/p>\n\n\n\n<p>\u00cen triunghiul dreptunghic fiecare catet\u0103 este egal\u0103 cu media geometric\u0103 dintre ipotenuz\u0103 \u0219i proiec\u021bia catetei pe ipotenuz\u0103. Fie triunghiul ABC cu C=90\u00b0 \u0219i CD perpendiculara pe AB. Exist\u0103 rela\u021bia:<\/p>\n\n\n\n<p><img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/32ff3faa2e9bf91298c72398ec3da5058a1682c8\" alt=\"{\\displaystyle BC^{2}=AB\\cdot BD}\">&nbsp;&nbsp; sau  <img decoding=\"async\" src=\"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/8a877ca4f681b092ed2b313a6f42c019fc8591fb\" alt=\"{\\displaystyle BC={\\sqrt {AB\\cdot BD}}}\"><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p>Fie ABC un <strong>triunghi oarecare<\/strong> \u0219i a, b, c lungimile laturilor [BC], [AC], respectiv [AB].  <strong><span class=\"has-inline-color has-vivid-red-color\">Aria triunghiului ABC<\/span><\/strong> poate fi calculat\u0103 cu una din formulele: A_ABC=(a\u22c5b\u22c5sin\u2061\u2221C)\/2 = (a\u22c5c\u22c5sin\u2061\u2221B)\/2 = (b\u22c5c\u22c5sin\u2061\u2221A)\/2 .<\/p>\n\n\n\n<p><strong><span class=\"has-inline-color has-vivid-red-color\"><a href=\"https:\/\/accesis.lpages.co\/meditatii-matematica-romana\/\">Vrei sa inveti rapid la matematica? Pregateste-te cu noi online. Intra pe pagina <\/a><\/span><\/strong><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Inva\u021b\u0103 matematic\u0103 a\u0219a cum trebuie. Meticulos, simplificat, explica\u021bii vizuale. Intr\u0103 pe site sau \u00eentreaba-ne detalii: office@accesis.ro<\/p>\n","protected":false},"author":1,"featured_media":2821,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false},"categories":[5],"tags":[49,51,50],"_links":{"self":[{"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/posts\/2383"}],"collection":[{"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/comments?post=2383"}],"version-history":[{"count":32,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/posts\/2383\/revisions"}],"predecessor-version":[{"id":2998,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/posts\/2383\/revisions\/2998"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/media\/2821"}],"wp:attachment":[{"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/media?parent=2383"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/categories?post=2383"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/accesis.ro\/blog\/wp-json\/wp\/v2\/tags?post=2383"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}