As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) Verification: AC ‖ de; (2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, and explain the reason

As shown in the figure, the quadrilateral ABCD is a rectangle, ∠ EDC = ∠ cab, ∠ Dec = 90 ° (1) Verification: AC ‖ de; (2) Make BF ⊥ AC at point F through point B, connect EF, try to judge the shape of quadrilateral BCEF, and explain the reason

1、
prove:
∵ rectangle ABCD
∴AB∥CD
∴∠DCA=∠CAB
∵∠EDC=∠CAB
∴∠EDC=∠DCA
∴AC∥DE
2. Parallelogram BCEF
prove:
∵BF⊥AC
∴∠BFC=∠AFB=90
∵∠DEC=90,AC∥DE
∴∠ACE=180-∠DEC=90
∴∠ACE=∠BFC
∴BF∥CE
∵AB=CD,∠EDC=∠CAB,∠DEC=∠AFB=90
∴△ABF≌△DCE （AAS）
∴BF=CE
The parallelogram BCEF
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