Quadrilateral Congruence
Author: Peter Wiles

Show Angle DAB

Show Angle ABC

Show Angle BCD

Show Angle CDA

The points A', B', C', and D' can be freely moved anywhere. 
Select the checkboxes to reveal information about quad 
ABCD. Determine what combination of boxes need to be
checked so that the only quadrilateral that can be created
is one congruent to ABCD.

Show Side AB

Show Side BC

Show Side CD

Show Side DA

A = (-15.583636100447588, 1.9931280436327268)
B = (-8.483957779564786, 1.3284773072096558)
C = (-11.096411725077616, 6.989767452390482)
D = (-14.042854847830469, 6.766528787034782)
poly1, a, b, c, d = Polygon(A, B, C, D)
A' = (-5.795143436762363, -0.2727267396277424)
B' = (3.0870073136186766, -0.21230394540746325)
e = Ray(A', B')
f = Circle(A', a)
G = Intersect(f, e, 1.0)
a' = Segment(A', G)
C' = (2.9359503280679786, 7.64265930322883)
h = Ray(B', C')
k = Circle(B', b)
I = Intersect(k, h, 1.0)
b' = Segment(B', I)
D' = (-5.8555662309826415, 7.552025111898411)
j = Ray(C', D')
p = Circle(C', c)
K = Intersect(p, j, 1.0)
c' = Segment(C', K)
m = Ray(D', A')
q = Circle(D', d)
L = Intersect(q, m, 1.0)
d' = Segment(D', L)
α = Angle(B, A, D)
β = Angle(C, B, A)
γ = Angle(D, C, B)
δ = Angle(A, D, C)
F' = Rotate(B', α, A')
ε = Angle(B', A', F')
r = Ray(A', F')
I' = Rotate(I, β, B')
ζ = Angle(I, B', I')
s = Ray(B', I')
K' = Rotate(K, γ, C')
η = Angle(K, C', K')
t = Ray(C', K')
L' = Rotate(L, δ, D')
θ = Angle(L, D', L')
a_1 = Ray(D', L')
poly2, e_1, f_1, h_1, j_1 = Polygon(A', B', C', D')
o = false
u = false
v = false
w = false
g = false
i = false
l = false
n = false