# proof of pythagoras theorem?????

pls help me out

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It is easy to grasp and prove Pythogorous theorem by relating right angle triangles having "whole number sides lengths alone"!

3^2+4^2+5^2 is graphically explainable on computers.

(Rearrange it as 5^2-4^2= 3^2. Note that 3^2=9 and (5+4) = 9

Further, 5^2 is 25 and by a split of it as 13 and 12 we have (13^2-12^2) = 5^2

And so on, endless possibilities of (odd number)^2 split and relating to separate right angle triangles exists!

A circle of "radius 5" has 8 number of " x,y whole number points" (2 per 2D-quadrant) and another four points on x and y axes (where either a-'x' or a-'y' is zero). In all 12 points with "x and y as whole numbers".

Similarly a circle of "radius-13" too has 8 numbers x,y whole number points (2 per a- quadrants) and another four points on x and y axes (where either a -x or a- y is zero). In all 12 points exist with "x and y as whole numbers".

Above two triplets actually relates smaller near-zero number sets "3, 4, 5" and "5, 12, 13". And we have

3^2+4^2= 5^2.................(1) and "5" is a hypotanuse.

5^2+12^2= 13^2.............(2) 5 and 13 are hypotanuses.

We have 3 hypotanuses in above two formulae. '5' and '5,13'

"3, 4 and 12" are not hypotanuses in both formulae!

Now imagine a brick of size 3 units (height), 4 units (breadth) and 12 units (length). Said brick has volume 3* 4* 12 = 12^2 = 144 cubic units!

(3^2 +4^2 = 5^2 is not only an equality in between 'sum of square units of two sides' and 'a hypotanuse square unit' but also extends as a volume and surface area relations as stated herinafter!

We know that 12^2 cubic units is volume of brick!

Surface area of brick is 5*4*12 =240 sq units which is "5 multiplied by base area (48 sq units) /( 4 *12) " Said relations exist when said pair of triplets relate 'a brick size'!

Probably said relatins were knowingly fixed by first users of brick having 3 inches height, 4 anches wide and 12 inches long sizes! It reveals an ancient manner of proving utility of pythagorus theorem!

You may regard above facts as a practical application of pythogorus theorem. It also give an insight into "area and volume" relations, which has consistently helped users of theorem!

Regards!

Draw a right triangle ABC.Draw a perpendicular to the hypotenuse from the opposite vertex and then proof the theorem by similarity.

I can't give u the proof as I can't sketch the diagram but u can find it in any 10th standard book.

• Anonymous

Hi Annie, this is Kekin, ur new friend, here is ur answer,

This theorem may have more known proofs than any other (the law of quadratic reciprocity being also a contender for that distinction); the book Pythagorean Proposition, by Elisha Scott Loomis, contains 367 proofs.

& search this site

http://en.wikipedia.org/wiki/Pythagoras_theorem

Thanks,

bye!

Kekin

Source(s): kekin_patel@yahoo.com

Check this link. It has a very comprehensive list of proofs.

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

• 4 years ago

Draw a square ABCD where each side length a + b units long. Draw point X on AB so that AX = a and BX = b. Draw point Y on BC so that BY = a and CY = b. Draw point Z on CD so that CZ = a and DZ = b. Draw point W on AD so that DW = a and AW = b. Now connect points XYZW. Since <A = <B = <C = <D = 90, note that by SAS congruence theorem that triangles: WAX, XBY, YCZ, ZDW are congruent to each other. Thus, corresponding sides and angles are congruent. Then XY = YZ = ZW = WX. Thus, all side lengths are equal. Let c be this common side lenght. Also, <AWX = <BXY = <CYZ = <DZW and <AXW = <BYX = <CZY = <DWZ. Note that <AXW + <AWX + <WAX = 180 since the sum of angles in a triangle is 180. Then <AXW + <AWX + 90 = 180 since <WAX is a right angle. Then <AXW + <AWX = 90. Note that <AXW + <WXY + <BXY = 180 since A,X,B are collinear. Then <AXW + <WXY + <AWX = 180 since <BXY = <AWX. Then <WXY + 90 = 180 since <AXW + <AWX = 90. Then <WXY = 90. Thus, <WXY is a right angle. Similarly, <XYZ = <YZW = <ZWX = 90. Thus, all angles are equal to 90. Now since all sides are equal and all angles are equal we see that XYZW is a square with side length c. Let's compare the areas. Area of square ABCD is (a + b)^2. Now look at it as a sum of the four triangles and square XYZW. Then the area is 4 * (1/2)(ab) + c^2. Then (a + b)^2 = 4*(1/2)(ab) + c^2 a^2 + 2ab + b^2 = 2ab + c^2 a^2 + b^2 = c^2 DONE!

• Anonymous

The most common proof is the geometrical one:

http://en.wikipedia.org/wiki/Pythagorean_theorem

• Anonymous

The proof is more geometrical and logical... I cant really portray it with mathematics symbols or equations. It really needs to be done visually.

• Robin
Lv 4

there are many ways to prove it

do you have any givens?

eg

ab^2=bc^2+ca^2-2bc*ac*cosc

but when c=90 deg

=>pyth. is true

• Pranil
Lv 7