Pythagorean Theorem — a² + b² = c²
A right triangle has one 90° angle. The Pythagorean theorem (a² + b² = c²) relates its three sides: legs a and b, and hypotenuse c (opposite the right angle). Right triangles are fundamental in trigonometry, construction, and navigation.
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Pro Tip
To check if a triangle is a right triangle: compute a²+b² and c². If equal, it's a right triangle. Also: if a triangle's longest side satisfies c²>a²+b², it's obtuse; if c²<a²+b², it's acute.
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Did You Know?
The 3-4-5 right triangle was known to ancient Egyptians, who used knotted ropes with 12 equal spaces to create right angles for surveying land after Nile floods. This "rope-stretching" method is one of the earliest practical applications of the Pythagorean theorem.
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