62-5 Zbroj kutova u trokutu

Istraži koliko iznosi zbroj kutova u trokutu. 
Možeš pomicati točke A,B i C.

Kroz vrh C povucimo                        usporedan sa stranicom AB.

pravac

Pravci                   i                     presječnice su usporednih pravaca.

AC

Zbroji veličine kutova u trokutu

α

β

BC

Zbroj kutova u trokutu 

veličina kuta α

veličina kuta β

veličina kuta γ

veličina kuta α

veličina kuta β

veličina kuta γ

Razmisli možeš li bez zbrajanja veličina kutova odrediti
koliko iznosi zbroj veličina kutova u trokutu. Vrijedi li to za svaki tokut?

animiraj

A = (-3.6528719022039224, 2.2446043028145266)
B = (8.7723735779378, 0.23677774981738633)
C = (8.597779964633702, 7.4533137663868185)
mnogokut1, c, a, b = Polygon(A, B, C)
α, β, γ = Angle(mnogokut1)
kutA: round(α)
kutB: round(β)
kutC: 180° - kutA - kutB
pravacC = false
d = Line(C, c)
ac = false
e = Line(C, B)
f = Line(A, C)
g = Line(A, B)
rot = 0 (slider from 0 to 5, step 0.01)
pomak1 = If(rot ≤ 1, rot, 1)
pomak2 = If(rot ≤ 1, 0, If[(rot > 1) ∧ (rot ≤ 2), rot - 1, 1])
pomak3 = If(rot ≤ 2, 0, If[(rot > 2) ∧ (rot ≤ 3), rot - 2, 1])
pomak4 = If(rot ≤ 3, 0, If[(rot > 3) ∧ (rot ≤ 4), rot - 3, 1])
pomak5 = If(rot ≤ 4, 0, If[(rot > 4) ∧ (rot ≤ 5), rot - 4, 1])
B1 = Rotate(B, (-pomak1 * 180)°, A)
C1 = Rotate(C, (-pomak1 * 180)°, A)
kutA1 = Angle(B1, A, C1)
C2 = Translate(C1, Vector[pomak2 * Vector[A, C]])
B2 = Translate(B1, Vector[pomak2 * Vector[A, C]])
A2 = Translate(A, Vector[pomak2 * Vector[A, C]])
kutA2 = Angle(B2, A2, C2)
C3 = Rotate(C, (-pomak3 * 180)°, B)
A3 = Rotate(A, (-pomak3 * 180)°, B)
kutB3 = Angle(C3, B, A3)
C4 = Translate(C3, Vector[pomak4 * Vector[B, C]])
A4 = Translate(A3, Vector[pomak4 * Vector[B, C]])
B4 = Translate(B, Vector[pomak4 * Vector[B, C]])
kutB4 = Angle(C4, B4, A4)
bc = false
T2, D = Intersect(CircleArc[B, B + 0.3 * Vector[B, C], B + 0.3 * Vector[B, A]], AngularBisector[C, B, A])
T3, E = Intersect(CircleArc[C, C + 0.3 * Vector[C, A], C + 0.3 * Vector[C, B]], AngularBisector[B, C, A])
T1, F = Intersect(CircleArc[A, A + 0.2 * Vector[A, B], A + 0.2 * Vector[A, C]], AngularBisector[B, A, C])
kutaaa: "" + kutA + ""
kutbbb: "" + kutB + ""
kutccc: "" + kutC + ""
S1 = (10.78020013093494, -6.92156039565068)
S2 = (15.930711723405865, -7.910924204373908)
ug = 0.32 (slider from 0 to 1, step 0.01)
mnogokut2, h, i, j, k = Polygon(Corner[1], Corner[2], Corner[2] + ug * (Corner[3] - Corner[2]), Corner[1] + ug * (Corner[4] - Corner[1]))
va = false
vb = false
vc = false
animacija = false