Slide Me!

Reset

Class 9: Triangles
Angle Sum Property in a Triangle

Start Animation

Stop

Refresh

Drag to change Position of points A,B,C as you please.
and click “Start animation ”button. “Stop” and “Refresh” 
button can also be used if needed

∠A+∠B+∠C=180°

- BENNY VARGHESE
PGT Mathematics
JNV Pathanamthitta
KERALA-686511

b = 0 (slider from 0 to 15, step 0.001)
A = (-4.390117979976402, -0.9745339658849491)
B = (-1.9874735104023786, 1.6097057252266482)
O' = Dilate(A, If[1 < b ≤ 2, 2 - b, 0], B)
g_1 = Segment(O', A)
C = (1.5047422883970751, -0.8767519235185643)
O'_1 = Dilate(A, If[1 < b ≤ 2, 2 - b, 0], B)
O'_2 = Dilate(A, If[1 < b ≤ 2, 2 - b, 0], B)
P' = Dilate(B, If[2 < b ≤ 3, 3 - b, 0], C)
h_1 = Segment(B, P')
S = Dilate(C, If[3 < b ≤ 4, 4 - b, 0], A)
i_1 = Segment(C, S)
c_1 = Circle(A, 0.5)
R = Intersect(c_1, i_1)
δ: round(Angle[R, A, B], 0)
T = Rotate(R, If[4 < b ≤ 5, ((b - 4) * δ), δ], A)
e_1 = CircleSector(A, R, T)
c = Circle(B, 0.5)
A_1 = Intersect(g_1, h_1)
B_1 = Intersect(c, g_1, 1)
α: round(Angle[B_1, B, C], 0)
Q = Rotate(B_1, If[5 < b ≤ 6, ((b - 5) * α), α], B)
d = CircleSector(B, B_1, Q)
e = Circle(C, 0.5)
D = Intersect(e, i_1)
β: 180° - α - δ
E = Rotate(D, If[6 < b ≤ 7, ((-(b - 6)) * β), (-β)], C)
f = CircleSector(C, E, D)
g = Circle(A, 0.5)
F = Intersect(g, i_1)
G = Intersect(g, g_1)
h = CircleSector(A, F, G)
H = (6.687190533815464, -1.1002537346417296)
i = Line(H, xAxis)
A' = Dilate(A, If[7 < b ≤ 8, 8 - b, 0], H)
u = Vector(A, A')
h' = Translate(h, u)
C' = Dilate(C, If[8 < b ≤ 9, 9 - b, 0], H)
v = Vector(C, C')
k = Circle(C, 0.5)
I = Intersect(k, i_1)
J = Intersect(k, h_1)
p = CircleSector(C, J, I)
p' = Translate(p, v)
K = Point(i)
L = Point(i)
q = Circle(B, 0.5)
M = Intersect(q, g_1)
N = Intersect(q, h_1)
r = CircleSector(B, M, N)
γ = 3.141592653589793 rad (slider from 0 to 6.283185307179586, step 1)
O = Rotate(B_1, If[5 < b ≤ 6, ((b - 5) * α), α], B)
r' = Rotate(r, If[9 < b ≤ 10, ((b - 9) * γ)], B)
B' = Dilate(B, If[10 < b ≤ 11, 11 - b, 0], H)
P = Point(r')
U = Point(r')
V_1 = Point(r')
m = Line(A, B)
n = Line(B, C)
s = Circle(B, 0.5)
W, Z = Intersect(s, n)
C_1, V = Intersect(s, m)
t = CircleSector(B, V, W)
w = Vector(B, B')
t' = Translate(t, w)
j = Line(H, i_1)
D_1 = Point(j)
E_1 = Point(j)
l = Segment(H, D_1)
a = Segment(H, E_1)
ε = If(4 < b < 5, ((b - 4) * δ), δ)
η = If(5 < b < 6, ((b - 5) * α), α)
θ = If(6 < b < 7, ((b - 6) * β), β)
text3: "∠A=" + (LaTeX[ε]) + ""
text4: "∠B=" + (LaTeX[η]) + ""
text5: "∠C=" + (LaTeX[θ]) + ""