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Pythagoras theorem?
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Pythagoras theorem?
In mathematics, the Pythagorean theorem, or Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
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Pythagoras theorem?
Pythagoras Theorem
The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It is named after the ancient Greek mathematician Pythagoras.
Statement of the Theorem
In any right triangle:
The theorem states that:
a² + b² = c²
This means that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Understanding the Components
Applications of the Theorem
The Pythagorean theorem is widely used in various fields:
Example Calculation
If a right triangle has legs of lengths 3 cm and 4 cm:
The hypotenuse measures 5 cm, demonstrating the theorem’s application in finding unknown side lengths.
The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. It is named after the ancient Greek mathematician Pythagoras.
Statement of the Theorem
In any right triangle:
- a = length of one leg
- b = length of the other leg
- c = length of the hypotenuse (the side opposite the right angle)
The theorem states that:
a² + b² = c²
This means that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Understanding the Components
- Right Triangle: A triangle that has one angle measuring 90 degrees.
- Hypotenuse: The longest side of the right triangle, opposite the right angle.
- Legs: The two shorter sides that form the right angle.
Applications of the Theorem
The Pythagorean theorem is widely used in various fields:
- Construction: To calculate distances and heights.
- Navigation: For determining the shortest path.
- Physics: In problems involving vectors and motion.
Example Calculation
If a right triangle has legs of lengths 3 cm and 4 cm:
- Apply the theorem: 3² + 4² = c²
- Calculate: 9 + 16 = c² → c² = 25
- Find c: c = √25 = 5 cm
The hypotenuse measures 5 cm, demonstrating the theorem’s application in finding unknown side lengths.
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Pythagoras theorem?
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Pythagoras theorem? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Pythagoras theorem? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pythagoras theorem?.
Pythagoras theorem? for Class 7 2024 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about Pythagoras theorem? covers all topics & solutions for Class 7 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Pythagoras theorem?.
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