Download The Converse of AIA is False in Hyperbolic Geometry

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Transcript 
THE CONVERSE OF THE A I A THEOREM IS
FALSE IN THE POINCARE UPPER HALF-PLANE AND
FALSE IN HYPERBOLIC GEOMETRY!
Lines
and m are parallel and line t is a transversal.
The fact that these pairs of alternate interior angles are NOT CONGRUENT
shows that the CONVERSE OF THE ALT. INT. ANGLES THM is
false in Hyperbolic Geometry and false in the Poincare Upper Half-plane.
mAngle APQ = 90.17°°
mAngle BPQ = 89.83°°
mAngle PQD = 121.49°°
mAngle PQF = 58.51°°
F
A
P
C
t
Q
B
D
Poincaré Half-Plane
E
m
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