Konsep Dasar Teorema Pythagoras
Summary
TLDRThis video script delves into the historical origins and practical applications of Pythagoras' theorem. It explains that the theorem, which defines the relationship between the sides of a right-angled triangle, was known to the Babylonians and Egyptians long before Pythagoras. The theorem is crucial for calculating areas, taxes, inheritances, and constructing pyramids. The video also covers how to use the theorem to determine the type of triangle and calculate the height of various geometric shapes. It highlights the theorem's significance in trigonometry, architecture, woodworking, navigation, and everyday problem-solving, emphasizing its widespread utility.
Takeaways
- 📚 The Pythagorean theorem has been known and proven for a long time, with evidence dating back to the Babylonians around 1900-1600 BCE.
- 🌏 The theorem was independently discovered by different ancient civilizations, including the Egyptians, Indians, and Chinese.
- 🔍 The theorem is named after Pythagoras, a Greek philosopher and mathematician, who introduced it to the Greek society and made it widely known, despite not being the first to discover it.
- 📐 The Pythagorean theorem describes the relationship between the lengths of the sides of a right-angled triangle, specifically that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- 🧮 Mathematically, the theorem is expressed as (a^2 = b^2 + c^2), where a is the hypotenuse and b and c are the other two sides.
- 🔑 The theorem is only applicable to right-angled triangles, which have one angle measuring 90°.
- 🔍 There are different types of triangles based on the Pythagorean theorem: acute triangles (where all angles are less than 90°), obtuse triangles (with one angle between 90° and 180°), and right-angled triangles (with one angle exactly 90°).
- 🏗️ The Pythagorean theorem has practical applications in daily life, such as calculating land area for tax or inheritance purposes, building pyramids, and in navigation.
- 🎓 At the high school level, the theorem serves as a foundation for trigonometry.
- 🏙️ The theorem is not just for solving math problems in school; it is used by architects to calculate roof slopes, install sloping floors, and ensure right angles in carpentry work.
- 🌳 It can also be used to measure the height of buildings, towers, and cliffs, and to calculate the volume of a prism by finding its height.
Q & A
What is the Pythagorean theorem?
-The Pythagorean theorem describes the relationship between the lengths of the sides of a right-angled triangle. It states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
When was the Pythagorean theorem first discovered?
-The Pythagorean theorem was discovered and proven a long time ago. Historical records suggest that the Babylonians found combinations of Pythagorean triples between 1900 and 1600 BCE.
Why was the Pythagorean theorem important in ancient times?
-In ancient times, the Pythagorean theorem was useful for everyday life, such as calculating land area for tax or inheritance purposes, building pyramids, and dealing with water.
Why is the theorem named after Pythagoras instead of the Babylonians?
-Pythagoras was a Greek philosopher and mathematician who lived around the 6th century BCE. Although the theorem was known before his time, he was the first to introduce it to the Greek society and make it famous worldwide.
What is a Pythagorean triple?
-A Pythagorean triple consists of three positive integers a, b, and c, such that a² + b² = c². These are the lengths of the sides of a right-angled triangle.
How can you use the Pythagorean theorem to find the length of the hypotenuse?
-You can use the Pythagorean theorem to find the length of the hypotenuse (c) by using the formula c² = a² + b², where a and b are the lengths of the other two sides.
What are the different types of triangles in relation to the Pythagorean theorem?
-There are three types of triangles in relation to the Pythagorean theorem: acute triangles (where all angles are less than 90°), obtuse triangles (where one angle is between 90° and 180°), and right-angled triangles (where one angle is exactly 90°).
Can the Pythagorean theorem be used to calculate the height of other geometric shapes?
-Yes, the Pythagorean theorem can be used to calculate the height of other geometric shapes such as trapezoids, calculate diagonals in rectangles and squares, and find the height of a prism to calculate its volume.
What is the significance of the Pythagorean theorem in trigonometry?
-In high school mathematics, the Pythagorean theorem serves as a foundation for trigonometry, which is essential for understanding the relationships between the angles and sides of triangles.
How is the Pythagorean theorem applied in real-world scenarios?
-The Pythagorean theorem is used by architects to calculate roof slopes, by builders to ensure right angles in construction, by navigators to determine the shortest path to a location, and by surveyors to measure the height of trees, towers, and cliffs.
What are some common Pythagorean triples?
-Some common Pythagorean triples include (3, 4, 5), (5, 12, 13), and (7, 24, 25). These are sets of three numbers that satisfy the equation a² + b² = c².
Outlines
📚 Introduction to Pythagoras' Theorem
This paragraph introduces the Pythagorean theorem with a brief historical account of its origins. It explains that the theorem was known and proven by the Babylonians as early as 1900-1600 BCE, who discovered Pythagorean Triples and recorded them on four prisms. The theorem was also discovered independently by the Egyptians, Indians, and ancient Chinese. The paragraph highlights the practical applications of the theorem in daily life, such as calculating land area for taxes or inheritance, and in building pyramids. It also discusses why the theorem is named after Pythagoras, a Greek philosopher and mathematician, even though he was not the first to discover it. Pythagoras is credited with introducing the theorem to the Greek society and making it famous worldwide. The theorem is then described as a mathematical rule that can be used to determine the length of one side of a right-angled triangle, specifically the hypotenuse. The formula a² = b² + c² is introduced, where 'a' is the hypotenuse and 'b' and 'c' are the other two sides. The concept of Pythagorean Triples is also explained, which are sets of three positive integers that satisfy the theorem.
🔍 Applications of Pythagoras' Theorem
This paragraph discusses the various applications of Pythagoras' Theorem beyond just solving mathematical problems. It explains how the theorem can be used to determine the type of triangle based on the relationship between the lengths of its sides. For example, if the square of the longest side (hypotenuse) is less than the sum of the squares of the other two sides, it's an acute triangle; if it's greater, it's an obtuse triangle; and if it's equal, it's a right-angled triangle. The theorem is also used to calculate the height of a frustum, trapezium, or to find the diagonals of a rectangle and square. The paragraph further illustrates how Pythagoras' Theorem is fundamental to trigonometry and is used in practical applications such as architecture for calculating the slope of a house roof or the length of stairs, and by carpenters to ensure right angles in furniture making. It also mentions its use in navigation for ships and airplanes, and in measuring the height of buildings, towers, and cliffs. The paragraph concludes with an invitation for the audience to practice the theorem by completing a Pythagorean Triple and to use the 'Kejar Kita' app for further learning.
Mindmap
Keywords
💡Pythagorean Theorem
💡Hypotenuse
💡Right-Angled Triangle
💡Babilonian
💡Pythagorean Triple
💡Mesopotamia
💡Architect
💡Trigonometry
💡Navigation
💡Volume
💡Exercise
Highlights
The Pythagorean theorem was discovered and proven long before Pythagoras, dating back to the Babylonians around 1900-1600 BCE.
The theorem was also discovered independently by the ancient Egyptians, Indians, and Chinese.
Pythagoras was a Greek philosopher and mathematician who introduced the theorem to the Greek society and made it famous worldwide.
The Pythagorean theorem describes the relationship between the lengths of the sides of a right-angled triangle.
The theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
The theorem is mathematically expressed as a² = b² + c², where 'a' is the hypotenuse and 'b' and 'c' are the other two sides.
Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem.
The theorem can be used to determine the type of triangle: acute, obtuse, or right-angled.
The Pythagorean theorem is not only used for mathematical problems but also has practical applications in daily life, such as calculating land area for taxes or inheritance.
The theorem was used by ancient civilizations for practical purposes like building pyramids.
The Pythagorean theorem is fundamental to trigonometry and is used in high school mathematics.
Architects use the Pythagorean theorem to calculate the slope of roofs and to ensure that two lines form a right angle.
The theorem is used in navigation to determine the shortest path to a certain area.
The height of buildings can be calculated using the Pythagorean theorem.
The theorem can also be used to measure the height of trees, towers, and cliffs.
The Pythagorean theorem has many practical uses, including in architecture, navigation, and geometry.
The video encourages viewers to practice the theorem to remember it better and offers an app for additional practice.
Transcripts
halo halo teman kece kalau ngecek video
ini Pasti kalian mau tahu lebih lanjut
Apa yang dimaksud dengan teorema
Pythagoras sebelum mulai Kita dengerin
cerita dulu ya tentang asal-usul teorema
Pythagoras ternyata teorema Pythagoras
sudah ditemukan dan dibuktikan sejak
lama sekali Menurut Catatan sejarah
diantara tahun 1900 hingga 1600 sebelum
masehi suku Babilonia sudah berhasil
menemukan tiga kombinasi angka Tripel
pythagoras mereka mencatat penemuan itu
di empat prasasti yang ditemukan di
daerah ya setelahnya teorema ini juga
ditemukan secara terpisah oleh bangsa
Mesir India dan Cina kuno juga loh wah
kenapa ya orang-orang jaman dulu perlu
tahu teorema Pythagoras Oh ternyata cara
memang banyak kegunaannya
dalam kehidupan sehari-hari misalnya
untuk menghitung luas lahan untuk
keperluan pajak atau warisan atau
membangun piramida dan karena air eh
tapi kan pythagoras orang Yunani Kenapa
teoremanya bukan atas nama orang
Babilonia ya Iya kita gores memang
seorang filsuf dan matematikawan asal
Yunani yang hidup sekitar tahun 600-an
sebelum masehi ia dilahirkan ratusan
tahun setelah adanya prasasti
peninggalan Suku Babilonia itu tapi
memang kita gores Yang pertama
mengenalkan teorema ini ke masyarakat
Yunani dan membuatnya terkenal di
seluruh dunia karena itu sekarang semua
orang mengetahuinya dengan nama teorema
Pythagoras walaupun bukan ia yang
pertama kali menemukannya Nah sekarang
kita bahas ya teoremanya di seri video
serba tahu kali ini
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Hai Apa yang dimaksud dengan teorema
Pythagoras teorema Pythagoras
menggambarkan hubungan antara panjang
sisi-sisi segitiga siku-siku tepatnya Ia
adalah suatu aturan matematika yang
dapat digunakan untuk menentukan panjang
Salah satu sisi dari sebuah segitiga
siku-siku ingat ya teorema Pythagoras
hanya berlaku untuk segitiga siku-siku
yaitu segitiga yang salah satu sudutnya
90°
Hai teorema Pythagoras menyatakan bahwa
dalam suatu segitiga siku-siku jumlah
kuadrat dari sisi-sisi yang saling tegak
lurus = kuadrat dari sisi miringnya jika
ditulis secara matematis rumus
Pythagoras adalah a kuadrat = b kuadrat
ditambah C kuadrat a adalah sisi miring
yang berada di depan sudut siku-siku
sedangkan b dan c adalah dua sisi
lainnya yang tegak lurus dari rumus
tersebut kita bisa mendapatkan dua rumus
turunannya yaitu backup kuadrat sama
dengan a kuadrat dikurang C kuadrat dan
C kuadrat sama dengan a kuadrat dikurang
b kuadrat bilangan A B dan C pada
segitiga siku-siku dinamakan sebagai
Tripel pythagoras beberapa Tripel
pythagoras yang umum digunakan terlihat
seperti ditabel ini
Hai supaya lebih paham Yuk kita latihan
soal Berapakah panjang sisi miring
segitiga siku-siku berikut ini Sisi yang
ditanyakan adalah CV mirip kita misalkan
sebagai ah dan dua sisi lainnya sebagai
p&c sesuai teorema Pythagoras kuadrat
sisi miring atau aquadrat sama dengan
jumlah kuadrat dari sisi yang saling
tegak lurus yaitu backup kuadrat
ditambah C kuadrat bisa kita tulis
aquadrat = b kuadrat tambah y kuadrat
kemudian kita masukkan nilai dari b dan
c yang sudah diketahui menjadi ah
kuadrat = 5 kuadrat tambah 12 kuadrat x
kuadrat = 25 plus 144a kuadrat = 169
berarti A1 dengan akar dari 169 A = 13
di panjang sisi miring segitiga tersebut
adalah 13 mudahkan teorema Pythagoras
dapat digunakan untuk menentukan jenis
segitiga ada apa aja ya jadi segitiga
Yap betul ada segitiga lancip yang semua
sudutnya kurang dari 90° segitiga tumpul
yang salah satu sudutnya diantara 90°
sampai 180° dan segitiga siku-siku yang
salah satu sudutnya 90° jika diketahui
panjang tiga sisi segitiga maka dapat
kita misalkan sisi miring atau sisi
terpanjang dari segitiga adalah A dan
dua sisi lainnya adalah b&c segitiga
termasuk pertama jenis segitiga lancip
jika aquadrat kurang dari B kuat
Hai tambah C kuadrat yang kedua jenis
segitiga tumpul Jika a kuadrat lebih
besar dari b kuadrat + y kuadrat yang
ketiga jenis segitiga siku-siku jika
aquadrat = b kuadrat + y kuadrat
[Musik]
pythagoras juga dapat digunakan untuk
menghitung tinggi segitiga jajargenjang
trapesium atau menghitung diagonal pada
layang-layang dan belah ketupat dengan
mengetahui tinggi atau diagonal dari
bangun datar tersebut kita dapat
menghitung luas bangun datar pythagoras
juga digunakan untuk mencari tinggi
limas sehingga dapat dihitung volumenya
pada tingkat SMA teorema Pythagoras
menjadi dasar untuk materi trigonometri
pythagoras gak hanya digunakan untuk
menjawab soal-soal matematika di sekolah
loh
Hai seorang arsitek dapat menggunakan
pythagoras untuk menghitung kemiringan
atap rumah memasang lantai rumah di
lahannya miring memastikan dua jenis
membentuk sudut siku-siku atau
menghitung panjang tangga menuju lantai
dua pengrajin kayu juga menggunakan
pythagoras untuk membuat kusen pintu dan
jendela meja atau bingkai agar
benar-benar membentuk sudut siku-siku
sebuah kapal laut dapat menentukan jalan
terdekat ke suatu wilayah dengan
pythagoras hal yang sama juga dapat
digunakan untuk navigasi pesawat
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ketinggian gedung dapat dihitung dengan
rumus phytagoras dengan cara yang sama
kita juga dapat mengukur tinggi pohon
menara dan tebing Wah ternyata banyak ya
kegunaan dari pythagoras sekarang kamu
Coba jawab ya di kolom komentar lengkapi
bilangan Tripel pythagoras ini 3
ke-4 Nah selanjutnya apa nih A5B 6 c 7 d
8 supaya rumus phytagoras semakin nempel
dan gak cepat lupa yuk perbanyak latihan
soal jiwa site kejar kita the tide atau
bisa juga Melalui aplikasi kejar kita
yang bisa kamu download di playstore
kejar kita kejar ilmu meraih cita dalam
[Musik]
[Tepuk tangan]
hai ketuk menjeda
[Musik]
تصفح المزيد من مقاطع الفيديو ذات الصلة
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