Any triangle applies, with side a² + b² = c².
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides (a² + b² = c²).
It calculates areas of triangles using trigonometry.
It states that in any triangle, a² + b² always equals c².
Yes, it can be used for equilateral triangles.
No, it can only be used for right-angled triangles.
Yes, it is applied to isosceles triangles.
No, it can only be used for obtuse triangles.
To find the hypotenuse, use the formula: c = √(a² + b²), where a and b are the lengths of the other two sides.
Subtract a from b and take the square root.
Add a and b, then divide by two.
Multiply a and b and take the square root.
Equilateral triangles.
Scalene triangles.
Only right-angled triangles are applicable.
Isosceles triangles only.
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5
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No, you need all three sides.
Only when two angles are known.
Yes, if you know the hypotenuse and one leg, you can find the other leg using a² = c² - b² (or b² = c² - a²).
No, you need one angle and one side.
It is primarily theoretical with no real use.
The theorem is used in construction and navigation to calculate distances.
In mathematics, to multiply large numbers.
It helps in painting accurately on square canvases.
By checking if all sides are equal.
Measure the angles to check for 90 degrees.
Check if a² + b² = c² holds true for the side lengths given.
Ensure the perimeter is divisible by 3.
It states that only equilateral triangles satisfy a² + b² = c².
It demonstrates that all angles in a triangle add to 180 degrees.
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, the triangle is right-angled.
It implies that the sum of the squares of the sides is zero.
The basic Pythagorean Theorem applies to 2D but extensions like the 3D distance formula use similar concepts.
Yes, but only for spheres.
No, it is only for four-dimensional spaces.
Yes, directly without any modification.
A sequence of four numbers that satisfies a² + b² = c² + d².
A set of three positive integers a, b, and c that satisfy the equation a² + b² = c² is called a Pythagorean triple.
An angle that measures 90 degrees.
A triangle with all sides equal.
(2, 2, 3)
(7, 24, 25)
The set (5, 12, 13) is another Pythagorean triple.
(8, 15, 18)
It helps in calculating distances and is fundamental in trigonometry and algebra applications.
Because it determines the area of a rectangle.
It provides the exact value of π.
Because it defines the shortest path in circular motion.
To find the distance between two points, apply the Pythagorean Theorem to the differences in x and y coordinates.
To calculate the area of shapes, not distances.
It helps in finding the slope of a line.
To determine if a point is above or below the x-axis.
Only Ancient Egyptians were known to use it.
The theorem was used by ancient Babylonian and Chinese mathematicians, aside from Pythagoras.
Only ancient Greek cultures utilized this theorem.
It was used solely by early Roman architects.