The sum of the interior angles of a triangle is always 180 degrees.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².
It describes the relationship between angles and sides in non-Euclidean geometry.
For any triangle, the length of one side is equal to the sum of the lengths of the other two sides.
Euclid
Aristotle
Archimedes
The theorem is named after the ancient Greek mathematician Pythagoras.
In the formula, 'c' represents the length of the hypotenuse, which is the side opposite the right angle.
The measure of the smaller angle in the triangle.
The perimeter of the triangle.
The area of the triangle.
Yes, because 3² + 4² = 9 + 16 = 25, which is 5², confirming it is a right triangle.
No, because none of the sides are the same length, it is a scalene triangle.
Yes, because all angles form 45 degrees.
No, because nothing proves the angles add up to 90 degrees.
A set of three whole numbers a, b, and c is a Pythagorean triple if a² + b² = c² holds true.
The numbers should correspond to the perimeter of an isosceles triangle.
Two numbers should add up to make the third one.
They must be consecutive numbers.
One example is (5, 12, 13) since 5² + 12² = 13².
(6, 8, 10)
(7, 24, 25)
(10, 24, 26)
It is used to calculate the speed of light in physics.
It helps solve algebraic equations.
It can be used to determine distances between points or to check the squareness of structures like buildings.
It is irrelevant to real life applications.
10
15
Using the theorem: 9² + b² = 15², b² = 225 - 81 = 144, so b = 12.
13
It helps measure angles between coordinate axes.
It’s used in the distance formula to find the distance between two points in a plane.
It forms the basis of calculating slopes.
It determines the origin point of a plane.
Because the fundamental relationship a² + b² = c² only holds in right triangles.
Because non-right triangles violate Euclidean laws.
It can apply to any triangle, it's just used less often for non-right triangles.
Non-right triangles need a different version of this theorem.
It helps calculate resultant vectors, which can be used to find net forces or velocities.
It evaluates the decay of radioactive isotopes.
It measures potential energy differences.
It is used to solve quantum uncertainties.
The angle opposite the hypotenuse is a right angle (90 degrees).
The angle is always acute.
The angle is always obtuse.
The theorem does not relate to angles directly.
Yes, an extension called the 3D Pythagorean Theorem or space diagonal formula can be used.
No, it is strictly for two-dimensional cases.
Only if the dimensions are isometric.
Yes, but only within Euclidean flat spaces.
If a² + b² = c² is true for a triangle, then the triangle must be a right triangle.
If the triangle is equilateral, then a² + b² does not equal c².
If a triangle exists, then Pythagorean Theorem is invalidated.
If a² + b² is greater than c², then the triangle is obtuse.
Scalene triangle
Equilateral triangle
Obtuse triangle
It's a right triangle because 8² + 15² = 17².