Pythagoras Theorem

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In a right-angled triangle, the square on the hypotenuse is equal to the sum of the squares on the remaining two sides. If a triangle ABC has a right angle at B, then AC² = AB² + BC².

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The hypotenuse is the longest side of a right-angled triangle. It is the side opposite to the right angle (90°). In the Pythagoras theorem formula a² + b² = c², 'c' represents the hypotenuse.

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Buddhayan, an Indian mathematician (600 B.C.), developed a relationship between the squares on the sides of a right-angled triangle. However, the present form of this relationship is credited to the G

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Here, hypotenuse = 5 cm (longest side), other sides = 3 cm and 4 cm. According to Pythagoras theorem: 5² = 3² + 4². Calculating: 25 = 9 + 16 = 25. Since both sides are equal, the theorem is verified.

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Pythagorean triplets are three positive numbers a, b, and c (where c is the largest) such that a² + b² = c². Examples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25).

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If in any triangle, the square on the largest side is equal to the sum of the squares on the remaining two sides, then the triangle is a right-angled triangle, and the angle opposite to the largest si

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Using Pythagoras theorem: height² + base² = hypotenuse². Here: height² + 5² = 13². Solving: height² = 169 - 25 = 144. Therefore, height = √144 = 12 m. The ladder reaches 12 m high on the wall.

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Compare c² with a² + b²: (1) If c² = a² + b², the triangle is right-angled. (2) If c² > a² + b², the triangle is obtuse-angled. (3) If c² < a² + b², the triangle is acute-angled.