如图,在梯形ABCD中,BC∥AD,延长CB到E,使BE=AD,连接AE、AC,已知AE=AC.
![](http://hiphotos.baidu.com/zhidao/pic/item/d62a6059252dd42ac7be542c003b5bb5c8eab886.jpg)
(1)证明:梯形ABCD是等腰梯形;
(2)若AH⊥BC,AH=2,CE=6,则梯形ABCD的面积为______.
(1)证明:连接BD,∵BC∥AD,BE=AD,∴四边形AEBD是平行四边形,∴AE=DB,又∵AE=AC,∴AC=DB,∴梯形ABCD是等腰梯形;(2)∵AE=AC,AH⊥CE,∴S△ACE=12CE•AH=12×6×2=6,∵AD=BE,∴S△ABE=S△ADC∴梯形ABCD...