To every phythagorean triangle there an equal and opposite reflected One?

Question

Clarification=the square root of the hypotenous give 2 triangles?

Answer 1

Take, for example, a "3-4-5" right triangle,
There are two legs, one with a length of 3 units and one with a length of 4 units. It is rather trivial (considering the name of the triangle) to find the length of the hypotenuse, but,

Using the Pythagorean theorem,
(Length of hypotenuse)^2 = (3)^\2 + (4)^2
(Length of hypotenuse)^2 = 25
Length of hypotenuse = +5 or -5.
However, it does not make any sense to think of a negative value of length so the positive value is taken.

The length of the hypotenuse can be thought of as the magnitude of the resultant between two directional vectors. Magnitudes are always greater than or equal to zero, never negative.
Now whether the resultant is pointed in the "positive" or "negative" direction or not is a different store and of no concern of the magnitude.

Answer 2

I'm not sure what you mean by this. But if you take two congruent right triangles ("Pythagorean triangle" is not a term that I've ever seen before.), you can form a rectangle from them. The second triangle is not the "opposite" of the first one, but a simple rotation in one axis; the two triangles are identical, just oriented differently.

Answer 3

A right triangle

The opposite side

The adjacent sice

and opposite the ninty degree angle is the Hypotenuse

Answer 4

If you bisect the 90 degree angle, the areas will be different for each triangle If the other two angles are different.

Answer 5

Huh? Not sure what you are asking...