TEOREMA PYTHAGORAS : MATEMATIKA KELAS 8 SMP

SIGMA SMART STUDY
13 Jan 202126:30

Summary

TLDRThis video provides a comprehensive lesson on the Pythagorean theorem for Grade 8 students, explaining how to calculate the sides of right triangles using the formula c² = a² + b². It covers identifying triangle types, solving for unknown sides, and using Pythagorean triples. Special right triangles (45°-45°-90° and 30°-60°-90°) are explained with practical examples. The video also demonstrates real-life applications, such as calculating the shortest travel distance, stair lengths, and diagonals in geometric shapes. Through step-by-step explanations and examples, viewers gain a clear understanding of the theorem’s principles and practical uses.

Takeaways

  • 😀 The Pythagorean theorem is used to calculate the sides of a right triangle using the formula c² = a² + b², where c is the hypotenuse.
  • 😀 To find an unknown side of a right triangle, you can rearrange the formula: a² = c² - b² or b² = c² - a².
  • 😀 A triangle is right-angled if c² = a² + b², acute if c² < a² + b², and obtuse if c² > a² + b².
  • 😀 Worked examples demonstrate applying the theorem to rectangles, triangles, and finding unknown sides, including using square roots for calculations.
  • 😀 Pythagorean triples are sets of three integers that form the sides of a right triangle, e.g., (3, 4, 5), (5, 12, 13), and multiples like (6, 8, 10).
  • 😀 Special right triangles include 45°-45°-90° triangles (isosceles) where hypotenuse = leg × √2.
  • 😀 Another special triangle is 30°-60°-90°, where the hypotenuse = 2 × short side, and the long side = short side × √3.
  • 😀 Real-life applications of the Pythagorean theorem include calculating the shortest path in navigation, ladder lengths, and diagonals of rectangles or 3D shapes.
  • 😀 Example applications: Ladder to a window 8 m high across a 6 m garden → minimum ladder length = 10 m; a ship traveling 100 km west and 75 km south → shortest distance = 125 km.
  • 😀 Understanding Pythagorean triples and special triangles helps simplify calculations without repeated use of the square root formula.
  • 😀 Consistent labeling of triangle sides (a, b, c) and awareness of units (cm, m, km) is essential for accurate problem-solving.
  • 😀 Repetition and step-by-step explanation in the script ensure students grasp both formulas and applications of the Pythagorean theorem.

Q & A

  • What is the Pythagorean theorem used for?

    -The Pythagorean theorem is used to calculate the sides of a right triangle.

  • What is the formula of the Pythagorean theorem?

    -The formula is c² = a² + b², where c is the hypotenuse and a and b are the other two sides of a right triangle.

  • How can you determine the type of triangle using the Pythagorean theorem?

    -If c² = a² + b², the triangle is right. If c² < a² + b², the triangle is acute. If c² > a² + b², the triangle is obtuse.

  • How do you calculate the width of a rectangle if the length and diagonal are known?

    -Use the formula width = √(diagonal² - length²). For example, if length = 16 cm and diagonal = 20 cm, width = √(400 - 256) = 12 cm.

  • What are Pythagorean triples and give examples?

    -Pythagorean triples are sets of three integers that form the sides of a right triangle. Examples include 3, 4, 5; 5, 12, 13; 7, 24, 25; and multiples such as 6, 8, 10.

  • What is special about a 45°-45°-90° triangle?

    -It is an isosceles right triangle where the two legs are equal and the hypotenuse is the leg length multiplied by √2.

  • How are the sides of a 30°-60°-90° triangle related?

    -In a 30°-60°-90° triangle, the short leg is a, the long leg is a√3, and the hypotenuse is 2a.

  • How can the Pythagorean theorem be applied in daily life?

    -It can be used to calculate the shortest distance between points, the length of stairs, and the diagonals of flat or spatial shapes.

  • If a ship travels 100 km west and then 75 km south, what is the shortest distance it can actually travel?

    -The shortest distance is the hypotenuse of the right triangle formed, calculated as √(100² + 75²) = 125 km.

  • How do you find a missing side of a right triangle if the hypotenuse and one leg are known?

    -Use the formula of the Pythagorean theorem: missing side = √(hypotenuse² - known leg²).

  • What is the method to find the value of x in a right triangle with sides 8x, 6x, and hypotenuse 20?

    -Use the Pythagorean theorem: (8x)² + (6x)² = 20² → 64x² + 36x² = 400 → 100x² = 400 → x = 2.

  • Why is it useful to memorize Pythagorean triples?

    -Memorizing Pythagorean triples allows for quick calculation of triangle sides without having to square and take roots repeatedly.

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Related Tags
Pythagorean TheoremGrade 8 MathRight TrianglesSpecial TrianglesPythagorean TriplesMath LessonEducationDistance CalculationGeometryStudy GuideInteractive LearningMath Examples