{"id":166,"date":"2023-07-18T23:02:58","date_gmt":"2023-07-18T23:02:58","guid":{"rendered":"https:\/\/rumusmatematika.id\/?p=166"},"modified":"2023-11-17T07:24:57","modified_gmt":"2023-11-17T07:24:57","slug":"teorema-pythagoras","status":"publish","type":"post","link":"https:\/\/tuturpedia.com\/rumusmatematika\/teorema-pythagoras\/","title":{"rendered":"Rumus Lengkap Teorema Pythagoras Yang Mudsah Di Pahami"},"content":{"rendered":"

Teorema Pythagoras<\/a>: Pengertian, Rumus, dan Penerapannya<\/strong><\/h2>\n

Teorema Pythagoras adalah salah satu konsep dasar dalam matematika yang telah menjadi fondasi untuk berbagai bidang, termasuk geometri, fisika, dan rekayasa. Ditemukan oleh matematikawan Yunani kuno Pythagoras, teorema ini memberikan hubungan yang kuat antara panjang sisi-sisi segitiga siku-siku. Artikel ini akan menjelaskan secara mendalam pengertian teorema Pythagoras, rumusnya, serta penerapannya dalam berbagai konteks matematika.<\/p>\n

\"Teorema
Teorema Pythagoras<\/figcaption><\/figure>\n

Pengertian Teorema Pythagoras:<\/strong><\/h3>\n

Teorema Pythagoras dinyatakan sebagai hubungan antara panjang sisi-sisi segitiga siku-siku. Jika \ufffd<\/span>a<\/span><\/span><\/span><\/span><\/span>, \ufffd<\/span>b<\/span><\/span><\/span><\/span><\/span>, dan \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span> adalah panjang sisi-sisi segitiga, dengan \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span> sebagai panjang sisi miring (hipotenusa), dan \u2220\ufffd<\/span>\u2220<\/span>C<\/span><\/span><\/span><\/span><\/span> adalah sudut siku-siku, maka teorema Pythagoras menyatakan:<\/p>\n

\ufffd2+\ufffd2=\ufffd2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Penting untuk dicatat bahwa teorema Pythagoras hanya berlaku untuk segitiga yang memiliki satu sudut yang besarnya tepat 90\u2218<\/span>9<\/span>0\u2218<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n

Rumus Teorema Pythagoras:<\/strong><\/a><\/h3>\n

Rumus Teorema Pythagoras dapat ditulis dalam beberapa bentuk yang setara:<\/p>\n

    \n
  1. \ufffd2+\ufffd2=\ufffd2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
  2. \ufffd=\ufffd2+\ufffd2<\/span>c<\/span>=<\/span><\/span>a<\/span>2<\/span><\/span><\/span><\/span>+<\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
  3. \ufffd=\ufffd2\u2212\ufffd2<\/span>b<\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span>\u2212<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n
  4. \ufffd=\ufffd2\u2212\ufffd2<\/span>a<\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span>\u2212<\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n

    Setiap bentuk rumus ini dapat digunakan tergantung pada informasi yang diketahui tentang segitiga siku-siku tertentu.<\/p>\n

    Penerapan Teorema Pythagoras:<\/strong><\/h3>\n

    **1. Pengukuran Panjang Sisi Segitiga:<\/strong> Salah satu penerapan langsung dari teorema Pythagoras adalah untuk mengukur panjang sisi-sisi segitiga siku-siku. Misalnya, jika kita tahu panjang dua sisi segitiga, kita dapat menggunakan teorema Pythagoras untuk menghitung panjang sisi yang ketiga.<\/p>\n

    Contoh:<\/em> Dalam segitiga siku-siku dengan sisi-sisi \ufffd=3<\/span>a<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span> dan \ufffd=4<\/span>b<\/span>=<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>, kita dapat menggunakan teorema Pythagoras untuk menghitung panjang hipotenusa \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span>: \ufffd=32+42=9+16=25=5<\/span>c<\/span>=<\/span><\/span>32<\/span><\/span><\/span><\/span>+<\/span>42<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>9+<\/span>16<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>25<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/p>\n

    **2. Verifikasi Segitiga Siku-Siku:<\/strong> Teorema Pythagoras juga dapat digunakan untuk memverifikasi apakah suatu segitiga adalah segitiga siku-siku. Jika panjang sisi-sisinya memenuhi \ufffd2+\ufffd2=\ufffd2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>, maka segitiga tersebut siku-siku.<\/p>\n

    Contoh:<\/em> Jika kita memiliki segitiga dengan sisi-sisi \ufffd=6<\/span>a<\/span>=<\/span><\/span>6<\/span><\/span><\/span><\/span><\/span>, \ufffd=8<\/span>b<\/span>=<\/span><\/span>8<\/span><\/span><\/span><\/span><\/span>, dan \ufffd=10<\/span>c<\/span>=<\/span><\/span>10<\/span><\/span><\/span><\/span><\/span>, kita dapat menggunakan teorema Pythagoras untuk memverifikasi apakah itu segitiga siku-siku: 62+82=36+64=100=102<\/span>62<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>82<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>36<\/span>+<\/span><\/span>64<\/span>=<\/span><\/span>100<\/span>=<\/span><\/span>1<\/span>02<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    **3. Penerapan dalam Geometri Ruang:<\/strong> Teorema Pythagoras tidak hanya berlaku untuk segitiga siku-siku dalam geometri datar tetapi juga dapat diterapkan dalam konteks geometri ruang. Misalnya, ketika kita memiliki sebuah kubus, diagonal ruang kubus dapat dihitung menggunakan teorema Pythagoras.<\/p>\n

    Contoh:<\/em> Jika panjang sisi kubus adalah \ufffd<\/span>s<\/span><\/span><\/span><\/span><\/span>, maka diagonal ruang (\ufffd<\/span>d<\/span><\/span><\/span><\/span><\/span>) dapat dihitung menggunakan teorema Pythagoras: \ufffd=\ufffd2+\ufffd2+\ufffd2=3\ufffd2<\/span>d<\/span>=<\/span><\/span>s<\/span>2<\/span><\/span><\/span><\/span>+<\/span>s<\/span>2<\/span><\/span><\/span><\/span>+<\/span>s<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>3s<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    **4. Navigasi dan Pengukuran Jarak:<\/strong> Teorema Pythagoras memiliki aplikasi praktis dalam navigasi dan pengukuran jarak. Misalnya, jika kita bergerak sejauh \ufffd<\/span>x<\/span><\/span><\/span><\/span><\/span> ke timur dan \ufffd<\/span>y<\/span><\/span><\/span><\/span><\/span> ke utara, jarak horizontal yang sebenarnya yang telah ditempuh adalah \ufffd2+\ufffd2<\/span>x<\/span>2<\/span><\/span><\/span><\/span>+<\/span>y<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>.<\/p>\n

    Contoh:<\/em> Jika kita bergerak 3 km ke timur (\ufffd=3<\/span>x<\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span>) dan 4 km ke utara (\ufffd=4<\/span>y<\/span>=<\/span><\/span>4<\/span><\/span><\/span><\/span><\/span>), jarak sebenarnya yang telah ditempuh adalah: \ufffd=32+42=9+16=25=5<\/span>d<\/span>=<\/span><\/span>32<\/span><\/span><\/span><\/span>+<\/span>42<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>9+<\/span>16<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>25<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span><\/p>\n

    Contoh Soal dan Penyelesaiannya:<\/strong><\/h3>\n

    Contoh Soal 1:<\/strong> Dalam segitiga siku-siku dengan sisi-sisi \ufffd=5<\/span>a<\/span>=<\/span><\/span>5<\/span><\/span><\/span><\/span><\/span> dan \ufffd=12<\/span>b<\/span>=<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>, hitung panjang hipotenusa \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span>.<\/p>\n

    Penyelesaian:<\/strong> Menggunakan rumus teorema Pythagoras, kita dapat menghitung panjang hipotenusa: \ufffd=52+122=25+144=169=13<\/span>c<\/span>=<\/span><\/span>52<\/span><\/span><\/span><\/span>+<\/span>122<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>25+<\/span>144<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>169<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span>=<\/span><\/span>13<\/span><\/span><\/span><\/span><\/span><\/p>\n

    Jadi, panjang hipotenusa \ufffd<\/span>c<\/span><\/span><\/span><\/span><\/span> adalah 13.<\/p>\n

    Contoh Soal 2:<\/strong> Apakah segitiga dengan sisi-sisi \ufffd=9<\/span>a<\/span>=<\/span><\/span>9<\/span><\/span><\/span><\/span><\/span>, \ufffd=12<\/span>b<\/span>=<\/span><\/span>12<\/span><\/span><\/span><\/span><\/span>, dan \ufffd=15<\/span>c<\/span>=<\/span><\/span>15<\/span><\/span><\/span><\/span><\/span> adalah segitiga siku-siku?<\/p>\n

    Penyelesaian:<\/strong> Menggunakan teorema Pythagoras, kita dapat memeriksa apakah segitiga ini memenuhi hubungan \ufffd2+\ufffd2=\ufffd2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>: 92+122=81+144=225=152<\/span>92<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>1<\/span>22<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>81<\/span>+<\/span><\/span>144<\/span>=<\/span><\/span>225<\/span>=<\/span><\/span>1<\/span>52<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

    Karena \ufffd2+\ufffd2=\ufffd2<\/span>a<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>+<\/span><\/span>b<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> benar, dapat disimpulkan bahwa segitiga ini adalah segitiga siku-siku.<\/p>\n

    Kesimpulan:<\/strong><\/h3>\n

    Teorema Pythagoras merupakan salah satu konsep paling fundamental dalam matematika yang memiliki aplikasi luas dalam berbagai konteks. Kemampuannya untuk menghubungkan panjang sisi-sisi segitiga siku-siku memungkinkan kita untuk mengukur jarak, memverifikasi sifat geometris, dan menjelaskan fenomena fisik. Dengan memahami konsep teorema Pythagoras dan cara mengaplikasikannya, siswa dan peminat matematika dapat memperluas pemahaman mereka tentang dunia matematika dan memanfaatkannya dalam berbagai situasi kehidupan sehari-hari serta konteks ilmiah yang lebih canggih.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Teorema Pythagoras: Pengertian, Rumus, dan Penerapannya Teorema Pythagoras adalah salah satu konsep dasar dalam matematika yang telah menjadi fondasi untuk […]<\/p>\n","protected":false},"author":1,"featured_media":396,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066],"class_list":["post-166","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-rumus-matematika","tag-apa-itu-pythagoras","tag-apa-itu-teorema-pythagoras","tag-bunyi-teorema-pythagoras","tag-contoh-soal-pythagoras-kelas-8","tag-contoh-soal-rumus-phytagoras","tag-contoh-soal-teorema-pythagoras-kelas-8","tag-contoh-teorema-pythagoras","tag-dalil-pythagoras","tag-hukum-pythagoras","tag-materi-pythagoras","tag-materi-pythagoras-kelas-8","tag-materi-teorema-pythagoras-kelas-8","tag-pengertian-teorema-pythagoras","tag-pythagoras-adalah","tag-pythagoras-kelas-8","tag-pythagoras-rumus","tag-pythagoras-segitiga-siku-siku","tag-rangkuman-teorema-pythagoras-kelas-8","tag-rumus-pythagoras-kelas-8"],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/comments?post=166"}],"version-history":[{"count":4,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/166\/revisions"}],"predecessor-version":[{"id":727,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/posts\/166\/revisions\/727"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media\/396"}],"wp:attachment":[{"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/media?parent=166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/categories?post=166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tuturpedia.com\/rumusmatematika\/wp-json\/wp\/v2\/tags?post=166"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}