Given 
.
Construction: Construct midpoint of 
and
let it be point D. Construct midpoint of 
and
let it be point E. Construct 
so it is congruent
to . Connect points D and C, C and F, and F and A.
Proof: 
by SAS. (
by
construction. 
because vertical angles are
congruent. 
by construction). 
by CPCTC therefore,
is parallel to
by alternate interior
angles theorem converse. Similarly, 
is parallel to
. 
by alternate interior angles
theorem. Since 
(CPCTC) and
(by
construction), then
by transitivity. Then 
by SAS. Then 
by CPCTC and since
is one-half of 
then it must also
be half of 
.