2016년 3월 21일 월요일

Proof of Sum of Angles of A Triangle



Before you see this post,

see




[Pic. 1]

Use The parallel postulate, we can find those facts in [Pic. 1]




[Pic. 2]

There is a triangle.

0°<{α,β,γ}<180°




[Pic. 3]

We can draw like [Pic. 3] by




[Pic. 4]

let's draw l4 is parallel with l2.




[Pic. 5]


We can find sum of angles of the triangle by

facts in [Pic. 1].

α+β+γ = 180°

So, sum of angles of the triangle is 180°.





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