Why a Triangle is 180 degrees?

Question

Just curious, but can anybody prove to me why a triangle is 180 degrees? Thanks in advance.

Answer 1

it is a bit difficult to prove a geometric problem without using diagram, but i'll try and explain it, and you can draw it yourself
Firstly a full circle measures 360 degrees by definition
so automatically half a circle ie a straight line measures 180 and a quarter circle is a right angle measures 90
then
first you start by showing the sum of the angles of a right angle triangle is 180
to do this
1) draw a rectangle (you know the corners measure 90)
2) draw a diagonal ( which splits it into two right triangles)
3) in one of the corners that the diagonal cuts label one of the angles x, so the other must be 90 - x since that corner measures 90 degrees
4) since the sides of the rectangle are parallel and the diagonal is a transversal, you can use the law of alternate angles to label the other corner with 90-x and x
5) add the angles of one of the right triangles
90 + (90-x) + x = 180
ends the proof for right triangles
next
for the real proof we will use this knowledge
1) Draw a triangle, (make its base the longest side so that it looks like a hat, that way you will understand my explanation)
2) label the left and right angles at the bottom x and y respectively
3) split the triangle into two right triangles (down the 'center' form the point at the top to the base)
4) using the previous proof you can then label each of the angles left and right of the split as 90-x and 90-y respectively
5) now add all the angles
x + y + (90-x) + (90-y) = 180 and your done

the end
.

Answer 2

Toothpicks and "it just is" arent very convincing proofs.

To answer youre question... well, I cant... but Euclid can. Look up Euclids postulates... Im sure he has a proof somewhere.

Anyway... all Euclid proved is that the angles of a triangle form half a circles measure. if you're asking why is it "180" and not "200"... that is arbitrary. It is a half circles measure by law... by geometry, by nature... but we assign "180 degrees" to equal half a circles measure by convention, by standardization.

That is the nature of the "degree"... just as π would be the value of half a circle in radian measure... or 200 in grads... or 2174 in Cogito's Angle Units. It doesnt matter. All that matters is the nature of the units being used and what half a circle equates to.

Answer 3

Because if you lay the parts of a triangle flat, they form a straight line, which would be a 180 degree angle.

Answer 4

it just is. it's a rule. and when you add up all the angles of absolutely any triangle, you will get 180.