Isosceles Triangle Problem

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April 5th 2006, 03:00 PM
Kitty_Kat

Isosceles Triangle Problem

Is it possible that on an isosceles triangle if you put squares on the sides, that two of those squares will equal the third?

ie: If the side lengths were 3,3,5 the squares would be 3x3 , 3x3, and 5x5

Please help.
April 5th 2006, 06:27 PM
ThePerfectHacker

Quote:

Originally Posted by Kitty_Kat

Is it possible that on an isosceles triangle if you put squares on the sides, that two of those squares will equal the third?

ie: If the side lengths were 3,3,5 the squares would be 3x3 , 3x3, and 5x5

Please help.

Yes, but you cannot get rational (fraction or whole numbers) length of sides.
The general form is $x,x,x\sqrt{2}$ for example, $1,1,\sqrt{2}$
April 6th 2006, 01:50 PM
Kitty_Kat

Quote:

Originally Posted by ThePerfectHacker

Yes, but you cannot get rational (fraction or whole numbers) length of sides.
The general form is $x,x,x\sqrt{2}$ for example, $1,1,\sqrt{2}$

Do you think it's possible to explain it further? Maybe with pictures because it would help alot. I need to explain it with a picture and prove that this theory is right so any details would help.
April 6th 2006, 03:37 PM
ThePerfectHacker

Quote:

Originally Posted by Kitty_Kat

Do you think it's possible to explain it further? Maybe with pictures because it would help alot. I need to explain it with a picture and prove that this theory is right so any details would help.

I do not know what your math level is but I am going to keep its as simple as possible. You said that when you form squares and the sides and add them you get the square of the third side, thus, in algebraic terms,
$x^2+y^2=z^2$ - but this is the Pythagorean Theorem. Thus, we must have a right triangle. Now you said that it is isoseles. Thus, two sides are equal. Thus, two of the angles must also be equal. Since one angle is already 90 degrees the other two angles must add up to 90 degrees also because the sum of the angles of ANY triangle is 180. Thus, the other two angles must be 45 and 45. Finally, there is a theorem about a 45-45-90 triangle that says if the smaller sides are $x$ then the biggest side (hypotenuse) is $x\sqrt{2}$
April 6th 2006, 04:18 PM
Kitty_Kat

Quote:

Originally Posted by ThePerfectHacker

I do not know what your math level is but I am going to keep its as simple as possible. You said that when you form squares and the sides and add them you get the square of the third side, thus, in algebraic terms,
$x^2+y^2=z^2$ - but this is the Pythagorean Theorem. Thus, we must have a right triangle. Now you said that it is isoseles. Thus, two sides are equal. Thus, two of the angles must also be equal. Since one angle is already 90 degrees the other two angles must add up to 90 degrees also because the sum of the angles of ANY triangle is 180. Thus, the other two angles must be 45 and 45. Finally, there is a theorem about a 45-45-90 triangle that says if the smaller sides are $x$ then the biggest side (hypotenuse) is $x\sqrt{2}$

Well I'm a grade 8 student. I think it's impossible for an isosceles triangle to be part of the pythegorean theorem because if two sides are always the same , as well as angles then wouldn't two of the sides always be equal leaveing the third side on it's own? So I think it's impossible but I need to prove it. The pythegorean Theorem may not work for isosceles triangles.
April 6th 2006, 04:23 PM
ThePerfectHacker

Quote:

Originally Posted by Kitty_Kat

Well I'm a grade 8 student. I think it's impossible for an isosceles triangle to be part of the pythegorean theorem because if two sides are always the same , as well as angles then wouldn't two of the sides always be equal leaveing the third side on it's own? So I think it's impossible but I need to prove it. The pythegorean Theorem may not work for isosceles triangles.

The pythagorean theorem works for any right triangle.
April 6th 2006, 04:24 PM
Kitty_Kat

Quote:

Originally Posted by ThePerfectHacker

The pythagorean theorem works for any right triangle.

Not to be a pest but that means it would work for isosceles triangles as well?
But how can that be? :confused:
April 6th 2006, 04:28 PM
Jameson

Any right isosceles triangle is in the form of $x,x,x\sqrt{2}$ and thus the Pythagorean Thereom holds true. But if it isn't a right triangle then this theorem does not apply.
April 6th 2006, 04:35 PM
Kitty_Kat

Pythagorean Theorem

Could you give me a definition of the Pythagorean Theorem to help me with the explanation I'm currently writting?
April 6th 2006, 04:36 PM
Kitty_Kat

Quote:

Originally Posted by Jameson

Any right isosceles triangle is in the form of $x,x,x\sqrt{2}$ and thus the Pythagorean Thereom holds true. But if it isn't a right triangle then this theorem does not apply.

Thank you, this helps me alot.