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.

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- Apr 5th 2006, 03:00 PMKitty_KatIsosceles 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. - Apr 5th 2006, 06:27 PMThePerfectHackerQuote:

Originally Posted by**Kitty_Kat**

The general form is $\displaystyle x,x,x\sqrt{2}$ for example, $\displaystyle 1,1,\sqrt{2}$ - Apr 6th 2006, 01:50 PMKitty_KatQuote:

Originally Posted by**ThePerfectHacker**

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. - Apr 6th 2006, 03:37 PMThePerfectHackerQuote:

Originally Posted by**Kitty_Kat**

$\displaystyle x^2+y^2=z^2$- 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 $\displaystyle x$ then the biggest side (hypotenuse) is $\displaystyle x\sqrt{2}$ - Apr 6th 2006, 04:18 PMKitty_KatQuote:

Originally Posted by**ThePerfectHacker**

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. - Apr 6th 2006, 04:23 PMThePerfectHackerQuote:

Originally Posted by**Kitty_Kat**

- Apr 6th 2006, 04:24 PMKitty_KatQuote:

Originally Posted by**ThePerfectHacker**

Not to be a pest but that means it would work for isosceles triangles as well?

But how can that be? :confused: - Apr 6th 2006, 04:28 PMJameson
Any

**right isosceles triangle**is in the form of $\displaystyle x,x,x\sqrt{2}$ and thus the Pythagorean Thereom holds true. But if it isn't a right triangle then this theorem does not apply. - Apr 6th 2006, 04:35 PMKitty_KatPythagorean Theorem
Could you give me a definition of the Pythagorean Theorem to help me with the explanation I'm currently writting?

- Apr 6th 2006, 04:36 PMKitty_KatQuote:

Originally Posted by**Jameson**

Thank you, this helps me alot.