Pythagorean_Theorem_Presentation grade 8.pptx

Teorema Phytagoras kelas 8

1. Pythagorean Theorem Mathematics - Grade 8

2. Definition The Pythagorean Theorem is a rule in right-angled triangles that states: "The square of the hypotenuse is equal to the sum of the squares of the other two sides." Mathematically: c² = a² + b²

3. Conditions The Pythagorean Theorem only applies to right-angled triangles. It relates the lengths of the sides of a right triangle.

4. Example: Finding the Hypotenuse Given a = 3 and b = 4: c² = a² + b² = 3² + 4² = 9 + 16 = 25 c = √25 = 5 So, the hypotenuse is 5 units.

5. Example: Finding a Side Given c = 13 and a = 5: b² = c² - a² = 13² - 5² = 169 - 25 = 144 b = √144 = 12 So, the other side is 12 units.

6. Pythagorean Triples Pythagorean Triples are sets of three whole numbers that satisfy the Pythagorean Theorem. Examples: - (3, 4, 5) - (5, 12, 13) - (7, 24, 25) - (8, 15, 17)

7. Real-Life Applications • Calculating diagonal distances • Estimating heights of buildings • Used in architecture, navigation, and engineering

8. Practice Questions 1. A right triangle has legs of 6 cm and 8 cm. Find the hypotenuse. 2. A ladder is 15 meters long and its base is 9 meters from the wall. How high does it reach on the wall?