# Consider a triangle with sides, $3,4,5$, does $3^2+4^2=5^2$ hold for such a triangle. [closed]

Consider a triangle with sides, $3,4,5$, let the angle opposite the greatest side $5$ be $\theta$, does $3^2+4^2=5^2$ hold for such a triangle. Now consider a triangle with sides (1,1,$\sqrt{2}$), let $\beta$ be the angle opposite the largest side $\sqrt{2}$. Is $\theta=\beta$.

-

## closed as unclear what you're asking by Jonas Meyer, Jeremy Rickard, drhab, Crostul, user91500Jun 10 at 12:21

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

$3^2 + 4^2 = 5^2$ based on arithmetic, not geometry. –  Arthur Fischer Aug 14 '12 at 4:52
I'm not sure why you're asking this to begin with... unless the Pythagorean theorem isn't something you're familiar with. –  Guess who it is. Aug 14 '12 at 4:53
This is true arithmetically but can it be represented geometrically. –  Rajesh K Singh Aug 14 '12 at 5:13
can we represent the lengths, $3,4,5$ on a plane exactly. i mean does the physical representation of a triangle of sides $3,4,5$ measure $3,4,5$ exactly(with no error). –  Rajesh K Singh Aug 15 '12 at 1:11
You're trolling, right? –  WacDonald's Aug 15 '12 at 1:44

Answer 1: Since if each side of a triangle has the same length as a corresponding side of the other triangle then the triangles are congruent it holds that your triangle is congruent to a right triangle with sides $3,4,5$ and thus the Pythagorean Theorem applies.

Answer 2: use trigonometry to calculate all angles, given that you know all the lengths

-
can we represent the lengths, $3,4,5$ on a plane exactly. i mean does the physical representation of a triangle of sides $3,4,5$ measure $3,4,5$ exactly(with no error). –  Rajesh K Singh Aug 15 '12 at 1:11
@RajeshKSingh: That's a question about Physics. The answer, in our current state of knowledge, is no. –  André Nicolas Aug 15 '12 at 4:40

Hint: Converse of Pythagorean Theorem. If $a^2+b^2=c^2$, where $a$, $b$, and $c$ are positive, then there is a triangle with sides $a$, $b$, and $c$, and the angle opposite the side of size $c$ is a right angle.

Or else use the Pythagorean Theorem, and the fact that two triangles with corresponding sides equal are congruent (SSS).

-
–  user2468 Aug 14 '12 at 5:01
can we represent the lengths, $3,4,5$ on a plane exactly. i mean does the physical representation of a triangle of sides $3,4,5$ measure $3,4,5$ exactly(with no error). –  Rajesh K Singh Aug 15 '12 at 1:20