Question

different approaches of Pythagoras theorem​

Answer 1

Answer:

Step-by-step explanation:

The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. Named after the Greek mathematician Pythagoras:

If the lengths of the legs are a and b, and the length of the hypotenuse is c, then, a²+b²=c²

There are many different proofs of this theorem.

algebraic proof : based on linear relations:

the geometric proof : based upon comparison of areas

based upon the vector operation.

dynamic proof : based on mass and velocity

in Right angle triangle ABC

∠B = 90°

Lets draw AD⊥ BC

in ΔABC ≅  ΔBDC ( all angles are equal)

AC/BC  = BC/DC  = AB/BD

=> AC * DC = BC²   eq 1

in ΔABC ≅  ΔABD ( all angles are equal)

AC/AB  = BC/BD  = AB/AD

=> AC * AD = AC²   eq 2

Adding eq 1 & eq 2

AC (DC + AD) = BC² + AB²

=> AC ( AC) = AB² + BC²

=> AC² = AB² + BC²