如图,已知梯形ABCD中AD∥BC,AB=AD=DC=4,对角线AC⊥AB.求梯形ABCD的周长.

问题描述:

如图,已知梯形ABCD中AD∥BC,AB=AD=DC=4,对角线AC⊥AB.求梯形ABCD的周长.

∵AD=DC,∴∠DAC=∠DCA(1分)∵AD∥BC,∴∠DAC=∠ACB(1分)∴∠DCA=∠ACB(1分)∵AD∥BC,AB=DC,∴∠B=∠BCD=2∠ACB,(1分)∵AC⊥AB,∴∠B+∠BCA=90°,即3∠BCA=90°,∴∠BCA=30°,(1分)∴BC=2AB(1分...