如图,在梯形ABCD中,AD∥BC,AB=AD=DC,AC⊥AB,延长CB至F,使BF=CD. (1)求∠ABC的度数; (2)求证:△CAF为等腰三角形.
如图,在梯形ABCD中,AD∥BC,AB=AD=DC,AC⊥AB,延长CB至F,使BF=CD.
(1)求∠ABC的度数;
(2)求证:△CAF为等腰三角形.
(1)求∠ABC的度数;
(2)求证:△CAF为等腰三角形.
数学人气:381 ℃时间:2019-08-17 19:54:16
优质解答
(1)∵AD∥BC,∴∠DAC=∠ACB.∵AD=DC,∴∠DCA=∠DAC.∴∠DCA=∠ACB=12∠DCB.∵DC=AB,∴∠DCB=∠ABC.∴∠ACB=12∠ABC.在△ACB中,∵AC⊥AB,∴∠CAB=90°.∴∠ACB+∠ABC=90°.∴12∠ABC+∠ABC=90°.∴∠A...
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