A triangle has 180 degrees

First off where did humans get the idea of 360 degrees in a circle ?

What else in our lives has approximately 360 things in it ? Give up ? Days in a year !!

Yep we got our 360 degrees concept from the 365 days in year. What did they do with those extra 5 days ? Party or fiesta, the same way we celebrate New Years and 4th of July. (by they way in the business world there are 30 days in EACH month and 360 days in a year)

So what is half of this 360 degrees circle ? Yep, a line and therefore 180 degree in a line. And what is a quarter of a circle ? (You know North-West or South-East angles). Yep, that is 90 degrees. (and we call those perpendicular lines)

So a straight line has 180 degrees. Makes sense right ?

Now lets say we have 2 parallel lines (see the post on Euclid and parallel lines)

And these two parallel lines are crossed by a third line. (check out picture on side bar)

If two lines are parallel, then the alternate interior angles are equal.
(if line one is parallel to line two, then angle d = angle e)

Ok now you will need your own paper and pencil. Draw a triangle. Then draw a line through the top point of your triangle parallel to the base of the triangle.

Label the angles of the line on top, angle 1, angle 2 (the top angle of the triangle) and angle 3.

Do you agree that angles 1 + 2 + 3 = 180 degrees a straight line ?
(you might need your child or grandchild to help you with this. They have done this several times in school, i hope.)

Now comes the tricky part. Label the two "base angles" inside the triangle on the bottom, angle 4 and 5.

Here comes the magic of Euclid and his proofs. (Don't be scare you already got a 100 for the effort to read all this and wanting to just learn. Remember when we stop learning, we stop growing and we collect moss like a rock.)

So since the lines are parallel, the angle 1 = 4 and the angle 3 = 5 (these are called alternate interior angles like the picture shows on the side bar d = e).

So now in the equation 1 + 2+ 3 = 180, we can replace the 1 with the 4 and the 3 with the 5.

And WHALA, we get angles 4 + 2 + 5 = 180 which are the three angles of the triangle.
(if your picture worked and you got this proof, you deserve an ice cream, well done)

I once saw a 3rd grade teacher take a straw and ask the class how many degrees are there in a straight line. The class yell out "180 !!" and then the teacher folded the staw up into a triangle and asked and how many degrees does this triangle have now ? and the class yell, "180 degrees !!"

Another proof is to cut a Big triangle out of a piece of paper. And label the angles 1,2,3. Then cut the triangle into three pieces. Line up the angles 1, 2, 3 into a straight line. WHALA there is your proof. Angles 1 + 2 + 3 = 180.