{"id":302479,"date":"2021-11-01T12:03:43","date_gmt":"2021-11-01T05:03:43","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=302479"},"modified":"2022-10-14T14:16:29","modified_gmt":"2022-10-14T07:16:29","slug":"teorema-phytagoras","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/teorema-phytagoras\/","title":{"rendered":"Teorema Phytagoras – Pengertian, Rumus, dan Contoh Soal"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Ibu memiliki sebuah cetakan berukuran segitiga sama sisi. Berhubung tidak ada penggaris, kamu diminta oleh ibu untuk menentukan tingginya. Langkah apa yang akan kamu lakukan? Jawabannya adalah dengan menggunakan teorema Phytagoras. <\/span><\/p>\n\n\n\n

Nah, pada artikel ini Quipper Blog akan mengajak Quipperian untuk membahas teorema Phytagoras kelas 8. <\/span>Check this out<\/span><\/em>!<\/span><\/p>\n\n\n\n

Pengertian Teorema Phytagoras<\/strong><\/h2>\n\n\n\n

Teorema Phytagoras atau dalil Phytagoras adalah teorema atau dalil yang menyatakan bahwa jumlah luas persegi yang menempel pada kaki-kaki segitiga siku-siku sama dengan luas persegi yang menempel pada hipotenusanya. <\/span><\/p>\n\n\n\n

Itulah mengapa teorema ini juga bisa disebut Phytagoras segitiga. Teorema ini dikenalkan oleh seorang filsuf asal Yunani, yaitu Phytagoras.<\/span><\/p>\n\n\n\n

Pembuktian Teorema Phytagoras<\/strong><\/h2>\n\n\n\n

Lantas, bagaimana langkah pembuktian teorema Phytagoras? Perhatikan gambar berikut.<\/span><\/p>\n\n\n\n

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

Artinya,<\/span><\/p>\n\n\n\n

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

Berdasarkan gambar di atas, besaran <\/span>a<\/span><\/em> dan <\/span>b<\/span><\/em> menunjukkan kaki segitiga siku-siku. Sementara itu, besaran <\/span>c<\/span><\/em> menunjukkan hipotenusa. <\/span><\/p>\n\n\n\n

Hipotenusa adalah sisi terpanjang dari segitiga siku-siku yang letaknya tepat berhadapan dengan sudut siku-sikunya.<\/span><\/p>\n\n\n\n

Jika Quipperian perhatikan, terdapat keunikan yang bisa ditemukan pada ketiga persegi di atas, yaitu luas persegi kuning merupakan hasil penjumlahan luas persegi biru dan persegi hijau. <\/span><\/p>\n\n\n\n

Persegi biru menempel pada kaki segitiga yang panjang sisinya <\/span>a<\/span><\/em>, persegi hijau menempel pada kaki segitiga yang panjangnya <\/span>b<\/span><\/em>, dan persegi kuning menempel pada kaki segitiga yang panjangnya <\/span>c. <\/span><\/em><\/p>\n\n\n\n

Secara matematis, hubungan ketiganya akan membentuk rumus teorema Phytagoras yang dituliskan sebagai:<\/span><\/p>\n\n\n\n

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

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

Dari persamaan itu, apa sih kesimpulan yang bisa Quipperian dapatkan terkait bentuk Phytagoras pada segitiga siku-siku yang berwarna orange?<\/span><\/p>\n\n\n\n

Misalnya, segitiga siku-siku orange memiliki panjang sisi <\/span>a<\/span><\/em> = 8 cm, <\/span>b<\/span><\/em> = 6 cm. <\/span><\/p>\n\n\n\n

Apakah benar luas persegi kuning sama dengan hasil penjumlahan luas persegi biru dan hijau? Yuk, kita buktikan!<\/span><\/p>\n\n\n\n

Pertama, Quipperian harus mencari panjang sisi <\/span>c<\/span><\/em> segitiga orange dengan persamaan yang telah disebutkan sebelumnya.<\/span><\/p>\n\n\n\n

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

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

Jadi, panjang sisi <\/span>c <\/span><\/em>pada segitiga orange = 10 cm. <\/span><\/p>\n\n\n\n

Sisi persegi biru sama dengan sisi segitiga <\/span>a<\/span><\/em>, sisi persegi hijau sama dengan sisi segitiga <\/span>b<\/span><\/em>, dan sisi persegi kuning sama dengan sisi segitiga <\/span>c<\/span><\/em>. <\/span><\/p>\n\n\n\n

Dengan demikian:<\/span><\/p>\n\n\n\n

Luas persegi biru + luas persegi hijau = luas persegi kuning<\/span><\/p>\n\n\n\n

8<\/span>2<\/span><\/sup> + 6<\/span>2<\/span><\/sup> = 10<\/span>2 <\/span><\/sup>cm<\/span>2<\/span><\/sup><\/p>\n\n\n\n

64 + 36 = 100 cm<\/span>2<\/span><\/sup> <\/span><\/p>\n\n\n\n

100 cm<\/span>2<\/span> = 100 cm<\/span>2<\/span><\/sup>  (terbukti)<\/span><\/p>\n\n\n\n

Kesimpulannya, panjang sisi persegi kuning merupakan hipotenusa segitiga siku-siku orange.<\/span><\/p>\n\n\n\n

Ada satu hal yang harus Quipperian ingat bahwa tidak semua bilangan memenuhi persamaan tersebut. <\/span><\/p>\n\n\n\n

Hanya bilangan tertentu saja yang bisa memenuhinya. Nah, bilangan yang memenuhi persamaan tersebut disebut bilangan tripel Phytagoras.<\/span><\/p>\n\n\n\n

Tripel Pythagoras<\/strong><\/h2>\n\n\n\n

Pada pembahasan sebelumnya, Quipperian sudah mengenal adanya besaran <\/span>a<\/span><\/em>, <\/span>b<\/span><\/em>, dan <\/span>c<\/span><\/em>. Nah, ketiga besaran tersebut selalu berteman baik dan tidak bisa dipisahkan satu sama lainnya. <\/span><\/p>\n\n\n\n

Tiga buah bilangan buah yang bisa memenuhi persamaan <\/span>a<\/span><\/em>2<\/span><\/sup> + <\/span>b<\/span><\/em>2<\/span><\/sup> = <\/span>c<\/span><\/em>2<\/span><\/sup> disebut sebagai tripel Phytagoras. Cara mencari tripel Phytagoras adalah dengan memasangkan setiap bilangan. <\/span><\/p>\n\n\n\n

Jika jumlah kuadratnya sama dengan kuadrat bilangan yang lain, berarti dikatakan triple Phytagoras. Perhatikan contoh berikut.<\/span><\/p>\n\n\n\n

3, 4, 5<\/span><\/p>\n\n\n\n

3<\/span>2<\/span><\/sup> = 9 <\/span>-><\/span> a2<\/sup><\/span><\/em><\/p>\n\n\n\n

42<\/sup><\/span> = 16 <\/span>-><\/span> b2<\/sup><\/span><\/em><\/p>\n\n\n\n

52<\/sup><\/span> = 25<\/span> -><\/span> c2<\/sup><\/span><\/em><\/p>\n\n\n\n

Coba kamu cek, apakah <\/span>a2<\/sup><\/span><\/em> + <\/span>b2<\/sup><\/span><\/em> = <\/span>c2<\/sup><\/span><\/em> <\/span><\/p>\n\n\n\n

32<\/sup><\/span> + 42<\/sup><\/span> = 52<\/sup><\/span>?<\/span><\/p>\n\n\n\n

9 + 16 = 25 <\/span><\/p>\n\n\n\n

25 = 25 (memenuhi)<\/span><\/p>\n\n\n\n

Itu artinya, bilangan 3, 4, dan 5 merupakan triple Pythagoras.<\/span><\/p>\n\n\n\n

Apa <\/span>gak ribet<\/span><\/em>? Ya <\/span>ribet sih<\/span><\/em>, tapi kamu tidak perlu khawatir karena tersedia bilangan triple Phytagoras yang sudah dihitung oleh para ahli. <\/span><\/p>\n\n\n\n

Berikut ini sebagian kecil contoh bilangan tripel Pythagoras yang perlu kamu ketahui.<\/span><\/p>\n\n\n\n

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

Untuk membuktikan kebenaran tabel di atas, Quipperian bisa mencobanya, ya.<\/span><\/p>\n\n\n\n

Agar Quipperian semakin paham, yuk simak contoh soal teorema Phytagoras kelas 8 berikut ini.<\/span><\/p>\n\n\n\n

Contoh Soal 1<\/strong><\/h2>\n\n\n\n

Perhatikan gambar segitiga siku-siku EGF berikut. <\/span><\/p>\n\n\n\n

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

Jika panjang sisi EG = 5 cm dan sisi FG = 12, tentukan panjang sisi EF!<\/span><\/p>\n\n\n\n

Pembahasan:<\/strong><\/p>\n\n\n\n

Pertama, Quipperian harus tahu dulu persamaan yang akan digunakan untuk mencari sisi EF!<\/span><\/p>\n\n\n\n

Berdasarkan persamaan <\/span>a2<\/sup><\/span><\/em> + <\/span>b2<\/sup><\/span><\/em> = <\/span>c2<\/sup><\/span><\/em>, diperoleh:<\/span><\/p>\n\n\n\n

a<\/span><\/em> = FG<\/span><\/p>\n\n\n\n

b<\/span><\/em> = EG<\/span><\/p>\n\n\n\n

c<\/span><\/em> = EF<\/span><\/p>\n\n\n\n

sehingga:<\/span><\/p>\n\n\n\n

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

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

Jadi, panjang sisi EF adalah 10 cm.<\/span><\/p>\n\n\n\n

Contoh Soal 2<\/strong><\/h2>\n\n\n\n

Paman membuat layang-layang berbentuk segitiga sama kaki seperti gambar berikut.<\/span><\/p>\n\n\n\n

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

Panjangnya kayu yang dibutuhkan untuk menopang tinggi layang-layangnya adalah 8 cm. <\/span><\/p>\n\n\n\n

Jika panjang sisi AC = 12 cm, tentukan panjang kayu yang dibutuhkan  untuk menopang hipotenusanya!<\/span><\/p>\n\n\n\n

Pembahasan:<\/strong><\/p>\n\n\n\n

Layang-layang paman berbentuk segitiga sama kaki. Artinya, segitiga tersebut terdiri dari dua segitiga siku-siku yang ukurannya sama. Perhatikan gambar berikut.<\/span><\/p>\n\n\n\n

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

Di soal tertulis panjangnya AC = 12 cm. Sementara itu, tinggi layang-layang segitiga (BD) memotong sisi AC menjadi sama panjang, sehingga panjang AD = DC = 6 cm.<\/span><\/p>\n\n\n\n

Jika kayu yang dibutuhkan untuk menopang tinggi layang-layang (BD) = 8 cm, maka panjang kayu untuk hipotenusanya (BC atau BA) dirumuskan sebagai berikut.<\/span><\/p>\n\n\n\n

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

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

Oleh karena panjang BC = 10 cm, maka panjang BA = 10 cm.<\/span><\/p>\n\n\n\n

Jadi, panjang kayu untuk menopang hipotenusanya adalah 10 cm + 10 cm = 20 cm.<\/span><\/p>\n\n\n\n

Itulah pembahasan Quipper Blog kali ini. Semoga bisa bermanfaat buat Quipperian. <\/span><\/p>\n\n\n\n

Jika kamu ingin mendapatkan materi lanjutan tentang teorema Phytagoras, <\/span>kuy<\/span><\/em> gabung bersama <\/span>Quipper Video<\/strong><\/a>. Tunggu apa lagi, buruan temukan kode promonya dan rasakan manfaatnya. Salam Quipper!<\/span><\/p>\n\n\n\n

Penulis: Eka Viandari<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Ibu memiliki sebuah cetakan berukuran segitiga sama sisi. Berhubung tidak ada penggaris, kamu diminta oleh ibu untuk menentukan tingginya. Langkah apa yang akan kamu…<\/p>\n","protected":false},"author":99400369,"featured_media":302658,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[],"ppma_author":[679386827],"class_list":["post-302479","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"\nTeorema Phytagoras - Pengertian, Rumus, dan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Apa itu Teorema Phytagoras? simak pengertian dalam hubungan dengan segitiga siku siku serta rumus cara menghitung dilengkapi dengan contoh soal\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/teorema-phytagoras\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Teorema Phytagoras - 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