Sum of the angles in a triangle
Author: Duane Habecker
Date: 4/12/07

Directions:
1. Move the vertices of ∆ABC around.
2. Notice that the angles change when you move the vertices.
3. Pull the red slider to watch the animation.
4. What mathematical concept are you supposed to learn from this applet?

przesuń

$Suma \;miar \;   kątów  \; w \;  trójkącie$
              $wynosi \;  \; \textcolor{red}{180^0}$

pokaż

A = (-10.743101665058417, 9.261079660034314)
B = (-18, 3)
C = (-0.5464617204950394, 0.40119434234965357)
P, c, a, b = Polygon(A, B, C)
D = Midpoint(B, A)
E = Midpoint(A, C)
F = Midpoint(B, C)
Q, d, b_1, f = Polygon(B, F, D)
R, e, a_1, d_1 = Polygon(A, D, E)
S, e_1, f_1, c_1 = Polygon(F, C, E)
α = 0 rad (slider from 0 to 3.141592653589793, step 0.017453292519943295)
G = Midpoint(B, F)
B' = Rotate(B, α, G)
F' = Rotate(F, α, G)
D' = Rotate(D, α, G)
Q', d', b', f' = Polygon(B', F', D')
H = Midpoint(F, C)
F'_1 = Rotate(F, -α, H)
C' = Rotate(C, -α, H)
E' = Rotate(E, -α, H)
S', e', f'_1, c' = Polygon(F'_1, C', E')
u = Vector(A * α / 3.14, F * α / 3.14)
A' = Translate(A, u)
D'_1 = Translate(D, u)
E'_1 = Translate(E, u)
R', e'_1, a', d'_1 = Polygon(A', D'_1, E'_1)
β = Angle(F', B', D')
γ = Angle(E', C', F'_1)
δ = Angle(D'_1, A', E'_1)
g = false