∴∠BCD=45 =∠ABC,∠A+∠DCA=90,∠A+∠ABE=90,
∴DB=DC,∠ABE=∠DCA,
∫In△DBH and △DCA
∠BDH=∠CDA BD=CD ∠HBD=∠ACD,
∴△DBH≌△DCA,
∴BH=AC.
(2) connecting CG,
F is the midpoint of BC, DB=DC,
∴DF vertically divides BC,
∴BG=CG,
∵∠ABE=∠CBE,BE⊥AC,
∴∠AEB=∠CEB,
In △ABE and △CBE.
∠∠ AEB =∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠∠,
∴△ABE≌△CBE,
∴EC=EA,
In Rt△CGE, the square of BG-the square of GE = the square of EA is obtained by Pythagorean theorem.