H
E
E
L
E
M
E
N
T
S
as AB is to CD, so is E to F,
while
E is equal to CH, and F to AG,
therefore
as AB is to CD, so is CH to AG.
Therefore
in the parallelograms BG, DH the sides about the equal angles are reciprocally proportional.
But
those equiangular parallelograms in which the sides about the equal angles are reciprocally proportional are equal; [VI.4]
therefore
the parallelogram BG is equal to the parallelogram DH.
