Yahoo Answers: Answers and Comments for Proof of pythagoras theorem????? [Mathematics]
Copyright © Yahoo! Inc. All rights reserved.
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
From Annie
enUS
Sat, 02 Jun 2007 02:24:56 +0000
3
Yahoo Answers: Answers and Comments for Proof of pythagoras theorem????? [Mathematics]
292
38
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://s.yimg.com/zz/combo?images/emaillogous.png

From ?: Draw a square ABCD where each side length a + ...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Thu, 19 May 2016 05:56:29 +0000
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!

From Ronald: Understanding the Pythagoras Theorem. Click on...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Wed, 10 Dec 2014 03:28:51 +0000
Understanding the Pythagoras Theorem. Click on the link to Watch the VIDEO explanation:
http://bit.ly/1wcE4CI
Pythagoras Theorem
In a right  angled triangle, the square on the hypotenuse is equal to the sum of the squares on the sides containing the right angle.
Given ABC is a triangle with angle BAC is equal to 90 degrees
To prove that BC square is equal to AB square plus AC square
Construction On AB, BC and CA as sides describes squares ABFG, BCDE and ACKL respectively.
Draw AMN parallel to BE meeting BC at M and DE at N.
Join FC and AE.
The proof of the theorem are as follows
It is given that angle BAC is equal to 90 degrees
Angle BAG is equal to 90 degrees since it is one of the angles of square BAGF.
Therefore angle BAC plus angle BAG is equal to 180 degrees
Therefore CAG is a straight line
Angle ABF is equal to angle CBE since they are angles of squares and enhance each angle is equal to 90 degrees
Adding angle ABF to both sides
angle ABF plus angle ABC is equal to angle CBE plus angle ABC
This means angle CBF is equal to angle ABE
In triangles CBF and ABE, BF is equal to AB since they are the sides of the square BAFG
Recall the angle CBF is equal to angle ABE that we have proved earlier in the proof
BC is equal to BS since they are the sides of the square BCDE
Therefore, triangle CBF is congruent to triangle ABE by SAS congruency
Therefore, triangle CBF is equal to triangle ABE
But triangle CBF is equal to half square ABFG Since they have the same base BF and they are between the same parallels BF, CG.
Triangle ABE is equal to half rectangle BENM Since they have the same base BE and are between the same parallels BE and AN.
Therefore, BENM is equal to square ABFG Since triangle CBF equal to triangle ABE
Similarly, rectangle CDNM is equal to square ACKL
Therefore BENM plus CDNM is equal to square ABFG plus square AKCL
This means square BCDE is equal to square ABFG plus ACKL
Therefore, BC square is equal to AB square plus AC square
Thus, we have proved the theorem.

From Posiedon: give me a proof you are annie!!
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sun, 03 Jun 2007 07:37:06 +0000
give me a proof you are annie!!

From Rahul p: the square of diagonal=
the square of base+th...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sun, 03 Jun 2007 02:35:44 +0000
the square of diagonal=
the square of base+the square of height

From Pranil: See the answer given by Daniel & T.T.K.
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sun, 03 Jun 2007 01:03:49 +0000
See the answer given by Daniel & T.T.K.

From kkr: It is easy to grasp and prove Pythogorous the...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 07:38:45 +0000
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 5^24^2= 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 (13^212^2) = 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 2Dquadrant) 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 "radius13" 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 nearzero 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!

From Happy: Draw a right triangle ABC.Draw a perpendicular...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 05:42:26 +0000
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.

From Anonymous: Hi Annie, this is Kekin, ur new friend, here i...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 05:19:46 +0000
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

From Robin: there are many ways to prove it
in what grad...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:33:30 +0000
there are many ways to prove it
in what grade are you?
do you have any givens?
eg
ab^2=bc^2+ca^22bc*ac*cosc
but when c=90 deg
=>pyth. is true

From lgr_86: go to this website and read
http://www.cutt...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:32:47 +0000
go to this website and read
http://www.cuttheknot.org/pythagoras/index.shtml

From ????: Try
http://mathforum.org/isaac/problems/pyt...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:32:17 +0000
Try
http://mathforum.org/isaac/problems/pythagthm.html
http://www.cuttheknot.org/pythagoras/index.shtml
http://en.wikipedia.org/wiki/Pythagorean_theorem
Hope it helps

From Anonymous: The most common proof is the geometrical one:
...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:32:12 +0000
The most common proof is the geometrical one:
http://en.wikipedia.org/wiki/Pythagorean_theorem

From Daniel T: Check this link. It has a very comprehensive l...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:31:34 +0000
Check this link. It has a very comprehensive list of proofs.
http://www.cuttheknot.org/pythagoras/index.shtml

From ♠ Author♠: tHe proof is obvious.
I give 5 different proo...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:31:02 +0000
tHe proof is obvious.
I give 5 different proofs
http://en.wikipedia.org/wiki/Pythagorean_theorem#Proofs

From Anonymous: The proof is more geometrical and logical... I...
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
https://answers.yahoo.com/question/index?qid=20070602022456AA11Q0O
Sat, 02 Jun 2007 02:28:28 +0000
The proof is more geometrical and logical... I cant really portray it with mathematics symbols or equations. It really needs to be done visually.