Lesson Limitations To Triangles

Source code of 'Limitations To Triangles'

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

For All Polygons: Sum of Inner Degrees = {{{180(n - 2)}}} where 'n' is the number of sides
Also, the sum of the outer angles will always equal 360 degrees.
Triangle: {{{180(3 - 2)}}} = {{{180}}}
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^2 + b^2 = c^2}}} where 'b' and 'a' are the legs and 'c' is the hypotenuse
Due to this theorm, we have the distance formula ({{{d = sqrt((x2 - x1)^2 + (y2 - y1)^2)}}})
Let us think that one side is 13 (b = 13) and the other side is 7 (a = 7)
{{{a^2 + b^2 = c^2}}}
{{{49 + 169 = c^2}}}
+-{{{sqrt(218) = c}}} Hypotenuse can not be a negative length.
{{{sqrt(218) = 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 > b}}} if {{{A > 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(A)/a = sin(B)/b = sin(C)/c}}}
{{{sin(60(pi)/180)/a = sin(6(pi)/18)/b = sin((pi)/3)/c}}} a = b = c