maths problem- equilateral triangles

[Happymonkey]

Hi someone asked me 'how do you prove that a triangle is equilateral?' it has been confusing me for ages and wondered if anyone knew how you prove it?

[sft42]

Simple....if you have a protactor measure the internal angles...they all must be 60 degrees exactly....or failing that if you have a rule then measure the sides they all should be equal.

[lisaj]

That's not a mathematical proof... I can't remember this one but I have it somewhere so if I do find it I'll post it.

[Lynnieshell]

would folding it in half prove it. If it was truly equilateral, then it should be symetrical or am I making this up?

[sft42]

Lisaj of course it's a mathmatical proof...by definition an equilateral triangle must have three sides of the same length and if all three sides are equal then the internal angels must be the same i.e. 60 degrees. I can't see how it can fail to be proof?? if there are any maths teachers out there who can enlighten please do so.

[NickleArse]

Lynnieshell, some triangles that are not equilateral can be symetrical. But only an equilateral triangle can be folded in half from any point and be symetrical.

[rja211077]

it's not a mathematical proof because it involves measurement. it's an empirical proof. i'm not sure there is a mathematical proof as surely you would have to know either the length of the sides or the size of 2 out of 3 of the internal/external angles to an infinite number of decimal places (i.e. 100% accurate), which is impossible...right?

[NickleArse]

Surely in theory sft's answer is mathmatical proof. But as you say it would be difficult to put it into practice and draw one by hand 100% accurate. Maybe a computer would fair better?

[NickleArse]

And before anyone says anything I know I spelt Mathematical wrong...it's still early.

[gilf]

Mathematical proof is something very different from scientific proof. In science it goes something like this. I think that all monkey cannot talk, we looked at 10,000 monkeys and none of them talked. Therefore monkeys cannot talk. But this would not be mathematical proof as you need some sort of formula that can apply to all conditions (as you can see i'm neither a maths expert or scientist). I guess you could say that a monkeys vocal cords at not developed enough to ever generate speech (OK still not math proof but thats the general idea). In maths proof is proof not a load of experiments suggesting something is so likely that the reverse is impossible or at best unlikely.

[jeffbwood]

There are a number of mathematical formulae that one can use to prove that a triangle is equilateral. Though in order to do so you must know any of the following - the length of the three sides - the length of two sides and an internal angle - the length of one side and two internal angles etc etc etc this along with the sine or cosine rules can prove that a triangle is equilateral although requires an initial measurement. However, the easiest way is to find the centre of the triangle by using all three points to draw a straight line perpendicularly to the opposite side. After drawing all three lines they should intersect at exactly the same point for it to be truely equilateral. Is detention over now miss??!

[anthomson]

Try using a compass (bit more eloquent than a ruler), put the compass needle on one point of the triangle and the pencil on a second. Rotate the compass and it should pass thru the third point - verify the same is true for the other two points of the triangle.