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Pythagorus Theorem

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Published in: Mathematics | Mechanical | SAT
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Brief slides on Pythagorus theorem covering all aspects with solved examples.

Saima J / Doha

4 years of teaching experience

Qualification: Master of Science in Materials Engineering

Teaches: Chemical, Maths, Chemistry, Physics, Science, Advanced Maths, Science Projects

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  1. Pythagoras' Theorem Exploring Right-Angled Triangles
  2. • The famous theorem by Pythagoras defined the relationship between the three sides of a right triangle. Pythagorean Theorem says that in a right triangle, the sum of the squares of the two right-angle sides will always be the same as the square of the hypotenuse e. 25 16 +9=25
  3. Introduction • Pythagoras' Theorem is a fundamental principle in geometry, relating the sides of a right-angled triangle: •a2+b2=c2 • Where c is the hypotenuse (the longest side).
  4. Key Terms • - Hypotenuse: The side opposite the right angle, the longest side. • - Legs: The other two sides of the triangle. • - Right-Angled Triangle: A triangle with one 900 angle. 900
  5. The Formula • In a right-angled triangle: • This equation allows us to calculate the length of one side if the other two are known. 2 2 c
  6. Solved Example 1 • Find the hypotenuse of a triangle with legs 3 cm and 4 cm. • Solution: 32 + 42 c2 9+16 = c2 25 3 4
  7. Solved Example 2 • Find one leg of a triangle if the hypotenuse is 10 cm and the other leg is 6 cm. • Solution: 62 + b2 102 •36+b2=100 •b2=64 •b = 464=8 cm. a: 6 c=10 b:
  8. Practice Questions 1 1. Find the hypotenuse of a triangle with legs 5 cm and 12 cm. 2. Calculate the missing leg of a triangle with a hypotenuse of 13 cm and one leg of 5 cm. V
  9. Practice Questions Contd. •1. A ladder is 10 m long and leans against a wall. The foot of the ladder is 6 m from the wall. How high does the ladder reach on the wall? • 2. A square has a diagonal of 14 cm. Find the length of one side.
  10. Real-World Applications • - Architecture: Calculating distances in building designs. • - Navigation: Determining shortest paths. • - Sports: Analyzing trajectories in games.

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