(1)证明:∵∠ABC>∠BCE.(三角形的外角大于任何一个与它不相邻的内角)
∠DCE=∠BCE.(已知)
∴∠ABC>∠DCE.(等量代换)
又∵∠DCE>∠A.
∴∠ABC>∠A.(不等式的性质)
(3)∠CFA=(1/2)∠ABC.
证明:设∠CAF=x,∠DCF=y.
∵∠DCF=∠CAF+∠CFA=x+∠CFA.
∴2∠DCF=2x+2∠CFA;
又∠DCB=∠CAB+∠ABC=2x+∠ABC.
∵2∠DCF=∠DCB.(已知)
∴2x+2∠CFA=2x+∠ABC,得:∠CFA=(1/2)∠ABC.