set1: vertically opposite angles

set2: vertiaclly opposite angles

THEOREM:    IF TWO LINES INTERSECT EACH OTHER ,
 THEN THE VERTICALLY OPPOSITE ANGLES ARE EQUAL.

LINEAR PAIRS OF ANGLES

ANGLE1+ANGLE2=180
ANGLE2+ANGLE3=180
ANGLE3+ANGLE4=180
ANGLE4+ANGLE1=180

angle1_1 = 1.0297442586766543 rad (slider from 0 to 180°)
A = (3.8, 0.46)
B = (6.149079720429981, 0.5184576671397788)
B' = Rotate(B, angle1_1, A)
angle1 = Angle(B, A, B')
f = Line(A, B)
g = Line(B', A)
D = Point(f)
E = Point(g)
D' = Rotate(D, angle1_1, A)
angle3 = Angle(D, A, D')
angle4 = Angle(B', A, D)
angle2 = Angle(E, A, B)
a = true
b = true