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Solution of Mathematical Geometry Proof in Senior High School Entrance Examination
Connect GC, BG

∫ Quadrilateral ABCD is a parallelogram, ∠ ABC = 90.

∴ quadrilateral ABCD is a rectangle.

∫AF average score ∠ bad

∴∠DAF=∠BAF=45

∫∠DCB = 90,DF∨AB

∴∠DFA=45,∠ECF=90

∴△ECF is isosceles Rt△

G is the midpoint of EF.

∴EG=CG=FG

∫△ABE is isosceles Rt△, AB=DC.

∴BE=DC

∠∠CEF =∠GCF = 45→∠ Berg =∠DCG= 135

∴△BEG≌△DCG

∴BG=DG

∵CG⊥EF→∠DGC+∠DGB=90

And ≈DGC =≈BGE

∴∠BGE+∠DGB=90

∴△DGB is isosceles Rt△

∴∠BDG=45