Question

已知在梯形ABCD中,AD//BC,AB=AD=DC,AC⊥AB,将CB延长至点F,使BF=CD

已知在梯形ABCD中,AD//BC,AB=AD=DC,AC⊥AB,将CB延长至点F,使BF=CD
（1）求∠ABC的度数
（2）求证：△CAF是等腰三角形

Answer 1

1.解：梯形ABCD中,AD‖BC,AB=AD=DC ∴∠DCB=∠ABC
CD=AD ∴∠DCA=∠DAC AD//BC ∴∠DAC=∠ACB ∴∠DCA=∠ACB
∴∠DCB=∠ABC=2∠ACB 又∠CAB=90° ∴∠ACB=30° ∠ABC=60°
2.BF=CD ∴∠BFA=∠BAF=∠ABC/2=30° ∴∠F=∠ACF ∴AC=AF