Pythagoras theorem : 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.
Slide 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
Slide 3 : using the same length equal to AB or BC with the help of divider from point A, we find point D on hypotenuse.
Slide 4 : Now length DC is also equal to X . Let length DE be Y
Slide 5 : length BC is equal to (X+Y)
Slide 6 : now we take length (BC) as 1 unit.
Length (AC) will be 1.4142135 units.
Length (CE)= length (BC)=1unit
Length (AE) = length (AC) – length ( CE )= 0.4142135 units
& length ( CD)= length(AE)= 0.4142135 unit
Slide 7 : now length(DE) will be, 1units – 0.4142135units =0.5857865 units
here L(AE)=L(CD)=X=0.4142135 units …….. (1 )
L(DE) = y = 0.5857865 units ………(2)
L(AC) = (2X+Y)= 1.4142135 units ……(3)
L(BC)= (X+Y)= 1units ………(4)
Y is having a specific relationship with X
Slide 8 :
we have L(BC)= L(AB)=X+Y & we want to get L(AC)= (2X+Y) : we have L(BC)= L(AB)=X+Y & we want to get L(AC)= (2X+Y)
Slide 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.
Slide 11 :
Slide 12 : that’s all .I am 100% sure that this will be the core explanation for the Pythagoras theorem.