The figure shows a right triangle ABC (BC =
a, AB = c) with the squares ABDE and ACFG. Line BHJ is perpendicular to
BE. Line CK is perpendicular to BC. Lines BE and GA extended meet at M.
Lines BJ and EA extended meet at L. Lines LN and KP are perpendicular to
BJ. If A_{1}, A_{2}, A_{3}, A_{4}, A_{5},
A_{6}, A_{7}, A_{8}, and A_{9} are the
shaded areas, prove that (1)
,
(2)
,
(3) Area ABDE = Area AHLN + Area FJKP.
