how can we prove pythagoras theorem by cutting and pasting of paper? can u help me plz...?

Answer 1

The second person to answer your question is on the right track. But to make it a little simpler, don't draw your own squares, just use graph paper.

Suppose your right triangle is 3 units by 4 by 5. Cut out 3 squares of graph paper. One will be 3 x 3; the next is 4x4, and the last is 5x5. Then just count the number of little squares in each piece. You will find that the total number of squares in the largest piece will equal the number in the other two added together!

This will always be true for any right triangle (where one angle is 90 degrees), no matter how large or small. Amazing, no?

Answer 2

see first draw a right angle triangle in a paper and cut that.4 eg u take the pythagorean triplet 3,4,5(in cms).now draw 3*3 square,4*4square,5*5square in a paper and cut all the three squares.since we no 5square=3square+4square(pythagorous theorem)take the 5*5square paper and place it on the table.take the three*three square paper and keep the thing at the center of the big square already pasted in the shape of diamond.now 4 the 4*4 square draw th diagnols.
leave tat aside.
take the rightangle triangle which u hav already cut and paste on the paper.paste the square on all sides of appropriate measurements accordin 2 the sides..with the help of a setsquare or a compass draw a line parallel to the hypotenuse over the 4*4cm square passin through the center of the square(center=pthe point where the diagnols meet).now take the 4cm square out and cut tat in to 4 quadrilaterals which would be shown by the lines.
now take out the previous things tat 5*5cm square over which is placed the 3*3cm square in the shape of diamond in the center.take the 4 quadrilaterals of the 4*4cm square and paste in the remainin paret of the 5cm square.it exactly fits in 2 tat and thus pythgarous theorem is proved

Answer 3

follow these steps:::
1. Take a card board of size say 20 cm × 20 cm.
2. Cut any right angled triangle and paste it on the cardboard. Suppose its sides are a,
b and c.
3. Cut a square of side a cm and place it along the side of length a cm of the right
angled triangle.
4. Similarly cut squares of sides b cm and c cm and place them along the respective
sides of the right angled triangle.
5 label them
6. Join BH and AI. These are two diagonals of the square ABIH. The two diagonals intersect each other at the point O.
7. Through O, draw RS || BC.
8. Draw PQ, the perpendicular bisector of RS, passing through O.
9. Now the square ABIH is divided in four quadrilaterals. Colour them as shown in
10. From the square ABIH cut the four quadrilaterals. Colour them

refer 10 th standard lab manual

Answer 4

We can show that a2 + b2 = c2 using Algebra
Take a look at this diagram ... it has that "abc" triangle in it (four of them actually):

Area of Whole Square
It is a big square, with each side having a length of a+b, so the total area is:
A = (a+b)(a+b)
Area of The Pieces
Now let's add up the areas of all the smaller pieces:
First, the smaller (tilted) square has an area of A = c2

And there are four triangles, each one has an area of A =½ab
So all four of them combined is A = 4(½ab) = 2ab

So, adding up the tilted square and the 4 triangles gives: A = c2+2ab
Both Areas Must Be Equal
The area of the large square is equal to the area of the tilted square and the 4 triangles. This can be written as:
(a+b)(a+b) = c2+2ab
NOW, let us rearrange this to see if we can get the pythagoras theorem:
Start with: (a+b)(a+b) = c2 + 2ab

Expand (a+b)(a+b): a2 + 2ab + b2 = c2 + 2ab

Subtract "2ab" from both sides: a2 + b2 = c2

DONE!

Answer 5

Draw a right angle trangle on paper. Then make sqares on the three sides. First cut the sqares. The smaller two sqares are equal to the area of the bigger sqare. try to prove the same by cutting the small squares into few small sqares and paste the same in the bigger square. I think your pythagaras theorem tells the same matter.

Answer 6

shrink 3 squares, 3 x 3, 4 x 4, 5 x 5, and draw a a million" grid on each and each. Then make an excellent triangle, putting the 4" and 3" at ninety stages to one yet another. The 5" is the hypotenuse. this demonstrates it superbly (9 +sixteen = 25)

Answer 7

im not really sure.....
but the eygptians figured out the egyptian traingle but using a string(rope) with a length of 12 and put down each point (3ft, 4ft, 5ft,) at each corner of the traingle.
that prob doesn't help though...

Answer 8

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Answer 9

dont know