Can anyone prove the Pythagoras theorem?

Question

Make it understandable to a Grade 8 student.

Answer 1

One proof often seen uses two squares, one inside the other, with the points of the smaller square on the sides of the larger square. This leaves you with four congruent right triangles that are inside the larger square but outside the smaller square. Label the short sides of the right triangles a and b and call the hypotenuse c.

Now note that the sides of the large square have length (a + b). Therefore, one way to calculate the area of the large square is (a + b)^2 = a^2 + 2ab + b^2.

You'll see that the area of the large square is equal to the area of the small square plus the four triangles. Also note the sides of the small square have length c. So, another way to calculate the area of the large square is to add up the area of the small square plus the four trianges, i.e. c^2 + 4 * ab/2 = c^2 + 2ab.

Combining the two ways to calculate of the area of the large square, we get:

a^2 + 2ab + b^2 = c^2 + 2ab

which simplifies to:

a^2 + b^2 = c^2.

and there is your proof!

Answer 2

A long time ago, a Greek mathematician named Pythagoras said that if we ADD the square of each leg of a right triangle, the answer is the same as the hypotenuse that is also squared.

Since you are in 8th grade, I will use an example with regular number.

Say we have a right triangle with leg 1 = 3 feet and leg 2 = 4 feet and the hypotenuse = 5 feet.

I will ADD the square of each leg and I will also square the hypotenuse. After doing so, the answer will be the same on both sides of the equation.

leg 1 = 3 feet.

Squaring leg 1, I get 3 feet times 3 feet = 9 feet.

leg 2 = 4 feet.

Squaring leg 2, I get 4 feet times 4 feet = 16 feet.

So, leg 1 squared + leg 2 squared gave me 25 feet.

I will now square the hypotenuse, which is 5 feet.

Well, 5 feet times 5 feet = 25 feet.

I got 25 feet = 25 feet...THE SAME answer on BOTH sides of the equation. See what I mean?

In summary, when we ADD the square of BOTH legs of a right triangle, we get the same answer when squaring the hypotenuse.

Guido

Answer 3

The pythogagoras theorum:
In a right triangle, the square of the hypotenuse equals the sum of the square of its remaining 2 sides.
This means
imagine a triangle ABC
angle A=90 degrees and its opposite side is the hypotenuse
so hypotenuse is the side opposite to the 90 degree angle
to prove this
hypotenuse*hypotenuse=1st side * 1st side+ 2nd side * 2nd side
= b* b=a*a+c*c
= 10*10 = 6*6+8*8
= 100 =36+64
= 100 = 100
Hey im in seventh

Answer 4

You mean the Pythagoreum Theorum sweety? It's easy... you just have to understand which side is a, which side is b, and which side is c. The a-side- squared + the b-side-squared will equal the c-side-squared. The a side is the side that's leaning up, the b side is the base which is the one that lays on the floor, and the c-side is the hypotenuse which is the longest side of the triangle.

Answer 5

The formula for that is this:
a^2+b^2=c^2

I will show you an example:
8^2+6^2=10^2
64+36=100
100=100

I hope that was helpful!

Answer 6

I believe you mean the Pythagorean Theorem. If so, it's supposed to be something like; A(squared)+B(squared)=C(squared), where these are all sides of a triangle.
Supposing that one side (A) is multiplied by itself, and then added to the side NEXT to it (B) also multiplied by itself, is supposed to equal the last side (C) multiplied by itself as well.

Answer 7

tell ya what ill tell you the answer as soon as you look it up yourself because im sure that's what your teacher was thinking would happen when she gave you this for homework.

Answer 8

you can refer to all major basic maths text, they shld hv it......