如图,在△ABC中,D,E在直线BC上. (1)若AB=BC=AC=CE=BD,求∠EAC的度数; (2)若AB=AC=CE=BD,∠DAE=100°,求∠EAC的度数.
问题描述:
如图,在△ABC中,D,E在直线BC上.
(1)若AB=BC=AC=CE=BD,求∠EAC的度数;
(2)若AB=AC=CE=BD,∠DAE=100°,求∠EAC的度数.
答
(1)∵AB=BC=AC,∴△ABC是等边三角形,∴∠ACB=60.∵AC=CE,∴∠E=∠EAC.又∵∠E+∠EAC=∠ACB=60°,∴∠EAC=30°;(2)∵AB=AC,∴∠ABC=∠ACB,∵AB=BD,AC=CE,∴∠BAD=∠D,∠EAC=∠E,又∵∠ABC=∠BAD+∠D...