i've been given a project on pythagoras theoem in which i've to prove it through various methods.?

Question

i'am studying in class10th. board is CBSE. please advise me throug various useful websites or data.

Answer 1

use this link a couple

Answer 2

http://www.cut-the-knot.org/pythagoras/index.shtml

That website has a great many proofs of the Pythagorean Theorem.

Of course, not all of them will be of interest to you...

Pick out the ones that you understand.

Answer 3

there is too many to choos from. yet some them that I stay by technique of contain: everyone makes mistakes; in basic terms study from those that you do make. stay existence to the fullest daily; you not in any respect comprehend how a lot time you've left

Answer 4

in addition to the answers youve got allready, what the first episode of Carl Sagan's COSMOS. while your at it what all 13, he speaks of pythagoras in a few

Answer 5

1) Use co-ordinate geometry:
Draw a graph in 2-dimensions:
a)Draw 2 lines perpendicular to each other(eg: x+y=1 and -x+y=2)
b) Draw another line joining these Two(perpendicular) lines.
c)Let the point of intersection of the perpendicular lines be A,
point of intersection of the third line with the two perpendicular lines be B and C respectively.
d)Measure length AB, BC, CA using distance formula or by observation.
e)You will find BC^2=AC^2+AB^2, repeat for 3-4 sets of lines.

2)We know that,
(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 2(4n^3 + 2n+ 2n^2)
=>(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 8n^3 + 4n+ 4n^2
=>(2n^2+2n+1)^2=(4n^4 + 4n^2 + 8n^3)+ (1 + 4n+ 4n^2)
=>(2n^2+2n+1)^2=(2n^2+ 2n)^2 + (2n+1)^2
This relation will give values(3,4,5);(5,12,13);(7,24,25)
for values of n=1,2,3.........
They all satisfy the theorem
Hence, proved

3)Trigonometry:
Let there be a right-angled triangle ABC right-angled at A with angles:
[90 degrees, x degrees, (90-x )degrees]...........sum of angles in a triangle is 180 degrees

Now, Sin(x)=AB/BC (perpendicular/hypotenuse)...............(1)
and Cos(x)=AC/BC (base/hypotenuse)............................(2)
We know that [Sin(x)]^2 + [Cos(x)]^2 = 1
substituting values from (1) & (2)
=>[AB/BC]^2 + [AC/BC]^2=1
=>[AB^2 + AC^2]/BC^2=1
=>AB^2 + AC^2 = BC^2
HENCE PROVED.

4)There is one more method by vectors, but in 10th you'll not understand.

Answer 6

http://www.cut-the-knot.org/pythagoras/index.shtml

Answer 7

google it like I did!:

http://www.cut-the-knot.org/pythagoras/index.shtml

Answer 8

What is wrong with the textbook you already have? And some help from someone who understands it better?

Answer 9

http://www.cut-the-knot.org/pythagoras/index.shtml
get set go!

Answer 10

www.cut-the-Knot.org/pythagoras/index.shtml