1. Pythagoras theorem
Take one right angled triangle with its two side having the same length (other than hypotenuse). let it be ABC .AB & BC are two sides and AC is hypotenuse.

2. using a divider(mathematical instrument) taking length equal to AB or BC we find point E on the hypotenuse. let length AE be X

3. using the same length equal to AB or BC with the help of divider from point A, we find point D on hypotenuse.

4. Now length DC is also equal to X . Let length DE be Y

5. length BC is equal to (X+Y)

6. now we take length (BC) as 1 unit.
Length (AC) will be units.
Length (CE)= length (BC)=1unit
Length (AE) = length (AC) – length ( CE )= units
& length ( CD)= length(AE)= unit

7. now length(DE) will be, 1units – 0.4142135units =0.5857865 units
here L(AE)=L(CD)=X= units …….. (1 )
L(DE) = y = units ………(2)
L(AC) = (2X+Y)= units ……(3)
L(BC)= (X+Y)= 1units ………(4)
Y is having a specific relationship with X

9. we have L(BC)= L(AB)=X+Y & we want to get L(AC)= (2X+Y)

10. we find out the hypotenuse .this is all Pythagoras theorem.
1sq.+1sq. = (ur 2) sq. is the unit triangle of Pythagoras theorem
( sq. =square, ur =under root)
all other are multiplication of this unit.
Now what about the right angled triangle which is not having their two sides same length (other than hypotenuse).this type of triange share their hypotenuse with the triangle having both the sides equal length.

12. that’s all .I am 100% sure that this will be the core explanation for the Pythagoras theorem.