Angle sum of a triangle
Author: Radha

Move the points!

Demonstration.

Draw a line on any side

when you move the line up to
 the 3rd vertex,you will observe 
3 adjacent angles whose 
sum will be equal to 180°
Now can we prove 
Angle sum property of a Triangle?

Angle sum property of a Triangle

Move = -0.5 (slider from -0.5 to 1.5, step 0.005)
d_1 = If(Move < 0, 0, If[Move < 1, Move, 1])
C = (0.30753892456407633, 6.655744963279506)
B = (4.0865391008823115, 3.2999140775385856)
A = (1.3113358463986078, 2.611033837063909)
poly1, c, a, b = Polygon(A, B, C)
AngleB = Angle(C, B, A)
AngleA = Angle(B, A, C)
AngleC = Angle(A, C, B)
f = Line(B + d_1 * (C - B), c)
D = Intersect(b, f)
E = Intersect(a, f)
e = Ray(B, C)
F = Point(e)
G = Point(f)
H = Point(f)
δ = Angle(F, E, G)
g = Ray(A, C)
I = Point(g)
ε = Angle(H, D, I)
h = Line(A, B)
ζ = Angle(I, C, F)
d = false
Sum: AngleA + AngleB + AngleC
text3: "" + (LaTeX[AngleA]) + "+" + (LaTeX[AngleB]) + "+" + (LaTeX[AngleC]) + "=" + (LaTeX[Sum]) + ""
text4: "Angle A+angleB+AngleC=" + Sum + ""
α = Angle(A, C, B)
β = Angle(C, B, A)
γ = Angle(B, A, C)