如图,等腰△ABC中,AB=AC,∠BAC=36°,BC=1,点D在边AC上且BD平分∠ABC,设CD=x. (1)求证:△ABC∽△BCD; (2)求x的值. 答案: (1)证明:∵等腰△ABC中,AB=AC,∠BAC=36°,∴∠ABC=∠C=72°.∵BD平分∠ABC,∴∠ABD=∠CBD=36°.∵∠CBD=∠A=36°,∠C=∠C,∴△ABC∽△BCD.(2)∵∠A=∠ABD=36°,∴AD=BD.∵∠CBD=36°,∠C=72°,∴∠BDC=72°.∴BD=BC.∴AD=BD=BC=1.设CD=x,则有AB=AC=x+1.∵△ABC∽△BCD,∴=,即=,整理得:x2 Is your schoolbag too heavy? The e-schoolbag will help you. It is said that e-schoolbags are going to be brought into 21 in Chinese middle schools soon. Heavy schoolbags have been a serious 22 for a long time. But the e-schoolbag will 23 . An e-schoolbag is 24 lighter than a usual schoolbag. Perhaps, the e-schoolbag should be 25 an e-textbook. It is a small computer for students. It is as 26 as a usual book, 27 it can still have all the things for study, such as textbooks, exercise books and so on which can be made 28 chips(芯片) like stamps. The students can read the text page by page on the screen, take notes, or even send e-mails to their teachers. They only need to 29 the right chip into the e-schoolbag. Then they can use it. Some people say 30 e-textbooks can be easily broken, while others say it is not good for eyes. But only time will tell. ( )21.A.use B.useful C.used D.to use ( )22.A.idea B.problem C.question D.thought ( )23.A.work it out B.work out it C.work out D.work them out ( )24.A.very B.much C.too D.so ( )25.A.call B.calls C.called D.calling ( )26.A.small B.smaller C.smallest D.most small ( )27. A.and B.as C.or D.but ( )28.A.into B.from C.up D.of ( )29.A.bring B.get C.take D.put ( )30.A.if B.what C.that D.which