Lesson Limitations To Triangles

This Lesson (Limitations To Triangles) was created by by Nate(3500)

For All Polygons: Sum of Inner Degrees = 180%28n+-+2%29

where 'n' is the number of sides
Also, the sum of the outer angles will always equal 360 degrees.
Triangle: 180%283+-+2%29

The sum of the inner sides of a triangle has to equal 180 degrees; possible triangle angles:
90, 45, 45
90, 30, 60
60, 60, 60
80, 75, 25
75, 70, 35
*For Right Triangles:
Pythagoras's Theorm: a%5E2+%2B+b%5E2+=+c%5E2

where 'b' and 'a' are the legs and 'c' is the hypotenuse
Due to this theorm, we have the distance formula ( d+=+sqrt%28%28x2+-+x1%29%5E2+%2B+%28y2+-+y1%29%5E2%29

)
Let us think that one side is 13 (b = 13) and the other side is 7 (a = 7)
a%5E2+%2B+b%5E2+=+c%5E2

Hypotenuse can not be a negative length.
sqrt%28218%29+=+c

*In Any Triangle: The sum of any two sides is greater than the length of the last side.
Example Triangle:
Right Triangle with sides: 8 and 6
Pythagoras's Theorm states that the hypotenuse is 10
8 + 6 > 10
10 + 6 > 8
10 + 8 > 6
The theory is True.
*For All Triangles
a+%3E+b

remember that 'a' and 'b' are the lengths and 'A' and 'B' are the angles
*For Triangles with Equal Angles (60,60,60)
The length of all the sides will be equal.
To prove this, use the Law of Sines: sin%28A%29%2Fa+=+sin%28B%29%2Fb+=+sin%28C%29%2Fc

sin%28A%29%2Fa+=+sin%28B%29%2Fb+=+sin%28C%29%2Fc

sin%2860%28pi%29%2F180%29%2Fa+=+sin%286%28pi%29%2F18%29%2Fb+=+sin%28%28pi%29%2F3%29%2Fc

a = b = c

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