How to solve the Pythagorean theorem problems: theorem, proof, examples, and their solutions.
For a right triangle,
if legs: a, b and hypotenuse: c,
then a2 + b2 = c2.
This is the Pythagorean theorem.
(= Pythagoras' theorem)
Start from the right triangle
whose lengths of the legs are a and b,
and whose length of the hypotenuse is c.
Draw two squares using four of the right triangles.
The center quadrilateral's angle is a right angle,
because m∠(plain) + m∠(dot) + 90 = 180.
(See the right triangle's interior angles.)
Find the areas of both squares:
(purple square) = (a + b)2
(right square) = 4 × (1/2)ab + c2
= (4 × blue triangle) + (red square)
The areas of both squares are equal:
(a + b)2 = 4 × (1/2)ab + c2
(a + b)2 = a2 + 2ab + b2
Square of a sum
Legs: 3, 4
Legs: 5, x