{"id":2307,"date":"2025-05-09T19:13:46","date_gmt":"2025-05-09T16:13:46","guid":{"rendered":"https:\/\/cedra.academy\/?p=2307"},"modified":"2025-09-09T19:33:31","modified_gmt":"2025-09-09T16:33:31","slug":"teorema-lui-pitagora","status":"publish","type":"post","link":"https:\/\/cedra.academy\/?p=2307","title":{"rendered":"Teorema lui Pitagora"},"content":{"rendered":"\n
Teorema lui Pitagora – fundamentul geometriei dreptunghice PPTX<\/a>
Descarc\u0103<\/a><\/div>\n\n\n\n

<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Teorema lui Pitagora este una dintre cele mai cunoscute \u0219i importante teoreme din geometrie. Ea descrie o rela\u021bie fundamental\u0103 \u00eentre laturile unui triunghi dreptunghic.<\/p>\n\n\n\n

Enun\u021bul teoremei<\/h3>\n\n\n\n

\u00cen orice triunghi dreptunghic, p\u0103tratul lungimii ipotenuzei este egal cu suma p\u0103tratelor lungimilor catetelor.<\/strong><\/p>\n\n\n\n

Matematic, dac\u0103 triunghiul dreptunghic are catetele aaa \u0219i bbb, iar ipotenuza este ccc, atunci teorema se scrie astfel: c2=a2+b2c^2 = a^2 + b^2c2=a2+b2<\/p>\n\n\n\n

Explica\u021bie<\/h3>\n\n\n\n
    \n
  • Catetele<\/strong> sunt laturile care formeaz\u0103 unghiul drept (90\u00b0).<\/li>\n\n\n\n
  • Ipotenuza<\/strong> este latura opus\u0103 unghiului drept \u0219i este cea mai lung\u0103 latur\u0103 a triunghiului dreptunghic.<\/li>\n<\/ul>\n\n\n\n

    Aceast\u0103 rela\u021bie permite calcularea lungimii unei laturi necunoscute atunci c\u00e2nd se cunosc celelalte dou\u0103 laturi.<\/p>\n\n\n\n

    Exemple de aplicare<\/h3>\n\n\n\n
      \n
    1. Calcularea ipotenuzei:<\/strong>
      Dac\u0103 un triunghi dreptunghic are catetele de 3 cm \u0219i 4 cm, lungimea ipotenuzei se calculeaz\u0103 astfel: c2=32+42=9+16=25\u2005\u200a\u27f9\u2005\u200ac=5 cmc^2 = 3^2 + 4^2 = 9 + 16 = 25 \\implies c = 5 \\text{ cm}c2=32+42=9+16=25\u27f9c=5 cm<\/li>\n\n\n\n
    2. Calcularea unei catete:<\/strong>
      Dac\u0103 ipotenuza este de 13 cm, iar o catet\u0103 de 5 cm, cealalt\u0103 catet\u0103 se afl\u0103 astfel: b2=c2\u2212a2=132\u221252=169\u221225=144\u2005\u200a\u27f9\u2005\u200ab=12 cmb^2 = c^2 – a^2 = 13^2 – 5^2 = 169 – 25 = 144 \\implies b = 12 \\text{ cm}b2=c2\u2212a2=132\u221252=169\u221225=144\u27f9b=12 cm<\/li>\n<\/ol>\n\n\n\n

      Utiliz\u0103ri<\/h3>\n\n\n\n

      Teorema lui Pitagora este folosit\u0103 frecvent \u00een:<\/p>\n\n\n\n

        \n
      • Geometrie \u0219i trigonometrie;<\/li>\n\n\n\n
      • Construc\u021bii \u0219i arhitectur\u0103;<\/li>\n\n\n\n
      • Fizic\u0103 \u0219i inginerie, pentru calculul distan\u021belor;<\/li>\n\n\n\n
      • Via\u021ba de zi cu zi, de exemplu, \u00een determinarea diagonalei unui dreptunghi.<\/li>\n<\/ul>\n\n\n\n

        Curiozitate istoric\u0103<\/h3>\n\n\n\n

        Teorema \u00eei poart\u0103 numele celebrului matematician grec Pitagora<\/strong>, care a tr\u0103it \u00een secolul al VI-lea \u00ee.Hr. Totu\u0219i, dovezi arat\u0103 c\u0103 civiliza\u021bii mult mai vechi, precum egiptenii \u0219i babilonienii, cuno\u0219teau aceast\u0103 rela\u021bie \u0219i o foloseau practic.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        <\/p>\n\n\n\n

        <\/p>\n\n\n\n

        Fi\u0219\u0103 de lucru \u2013 Teorema lui Pitagora<\/h1>\n\n\n\n

        1. Teorema lui Pitagora<\/h2>\n\n\n\n

        Enun\u021b:<\/strong> \u00cen orice triunghi dreptunghic, p\u0103tratul lungimii ipotenuzei este egal cu suma p\u0103tratelor lungimilor catetelor. c2=a2+b2c^2 = a^2 + b^2c2=a2+b2<\/p>\n\n\n\n

          \n
        • aaa \u0219i bbb \u2013 catetele (laturile care formeaz\u0103 unghiul drept)<\/li>\n\n\n\n
        • ccc \u2013 ipotenuza (latura opus\u0103 unghiului drept)<\/li>\n<\/ul>\n\n\n\n

          Sugestie de desen:<\/strong> Triunghi dreptunghic cu p\u0103tratele construite pe fiecare latur\u0103.<\/p>\n\n\n\n

          2. Exemple explicative<\/h2>\n\n\n\n

          Exemplul 1 \u2013 Calculul ipotenuzei<\/strong><\/p>\n\n\n\n

            \n
          • Catetele: a=3 cm,b=4 cma = 3 \\text{ cm}, b = 4 \\text{ cm}a=3 cm,b=4 cm<\/li>\n<\/ul>\n\n\n\n

            c2=32+42=9+16=25\u2005\u200a\u27f9\u2005\u200ac=5 cmc^2 = 3^2 + 4^2 = 9 + 16 = 25 \\implies c = 5 \\text{ cm}c2=32+42=9+16=25\u27f9c=5 cm<\/p>\n\n\n\n

            Exemplul 2 \u2013 Calculul unei catete<\/strong><\/p>\n\n\n\n

              \n
            • Ipotenuza: c=13 cmc = 13 \\text{ cm}c=13 cm<\/li>\n\n\n\n
            • Catet\u0103 cunoscut\u0103: a=5 cma = 5 \\text{ cm}a=5 cm<\/li>\n<\/ul>\n\n\n\n

              b2=c2\u2212a2=169\u221225=144\u2005\u200a\u27f9\u2005\u200ab=12 cmb^2 = c^2 – a^2 = 169 – 25 = 144 \\implies b = 12 \\text{ cm}b2=c2\u2212a2=169\u221225=144\u27f9b=12 cm<\/p>\n\n\n\n

              3. Exerci\u021bii pentru elevi<\/h2>\n\n\n\n

              Exerci\u021biul 1<\/strong>
              Triunghi dreptunghic cu catetele a=6 cma = 6 \\text{ cm}a=6 cm \u0219i b=8 cmb = 8 \\text{ cm}b=8 cm.
              Calcula\u021bi lungimea ipotenuzei ccc.<\/p>\n\n\n\n

              Exerci\u021biul 2<\/strong>
              Triunghi dreptunghic cu ipotenuza c=10 cmc = 10 \\text{ cm}c=10 cm \u0219i o catet\u0103 a=6 cma = 6 \\text{ cm}a=6 cm.
              Calcula\u021bi cealalt\u0103 catet\u0103 bbb.<\/p>\n\n\n\n

              Exerci\u021biul 3 \u2013 Problema practic\u0103<\/strong>
              O scar\u0103 se sprijin\u0103 de peretele unei case astfel \u00eenc\u00e2t baza sc\u0103rii este la 3 m de perete, iar scara ajunge la o \u00een\u0103l\u021bime de 4 m pe perete.<\/p>\n\n\n\n

                \n
              • Care este lungimea sc\u0103rii?<\/li>\n<\/ul>\n\n\n\n

                4. Aplic\u0103ri practice<\/h2>\n\n\n\n
                  \n
                • Determinarea diagonalelor \u00een dreptunghiuri sau p\u0103trate.<\/li>\n\n\n\n
                • Construc\u021bii \u0219i amenaj\u0103ri (rampe, sc\u0103ri).<\/li>\n\n\n\n
                • Fizic\u0103 \u0219i inginerie: calculul distan\u021belor \u0219i traiectoriilor.<\/li>\n\n\n\n
                • Via\u021ba cotidian\u0103: m\u0103surarea unor spa\u021bii inaccesibile direct.<\/li>\n<\/ul>\n\n\n\n

                  5. Curiozitate istoric\u0103<\/h2>\n\n\n\n

                  Teorema poart\u0103 numele lui Pitagora<\/strong>, matematician grec din secolul VI \u00ee.Hr., \u00eens\u0103 civiza\u021bii egiptene \u0219i babiloniene foloseau aceast\u0103 rela\u021bie cu sute de ani \u00eenainte pentru construc\u021bii \u0219i m\u0103sur\u0103tori practice.<\/p>\n\n\n\n

                  \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

                  Teorema lui Pitagora este una dintre cele mai cunoscute \u0219i importante teoreme din geometrie. Ea descrie o rela\u021bie fundamental\u0103 \u00eentre laturile unui triunghi dreptunghic. Enun\u021bul teoremei \u00cen orice triunghi dreptunghic, […]<\/p>\n","protected":false},"author":1,"featured_media":2308,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,10],"tags":[],"_links":{"self":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/2307"}],"collection":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2307"}],"version-history":[{"count":1,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/2307\/revisions"}],"predecessor-version":[{"id":2315,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/posts\/2307\/revisions\/2315"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=\/wp\/v2\/media\/2308"}],"wp:attachment":[{"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2307"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2307"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cedra.academy\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2307"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}