题目

已知△ABC是等边三角形，P为△ABC所在平面内一个动点，BP=BA，若0°﹤∠PBC﹤ 180°，且∠PBC的平分线上一点D满足DB=DA. （1） 当BP和BA重合时(如图1)，则∠BPD=°； （2） 当BP在∠ABC内部时(如图2)，求∠BPD的度数； （3） 当BP在∠ABC外部时，请直接写出∠BPD的度数，并画出相应的图形. 答案：【1】30 解： 连接CD，∵DB是∠PBC的平分线 ，∴∠PBD=∠CBD ，∵△ABC是等边三角形 ，∴AB=BC=CA，∠ACB=60°。∵BP=BA ，所以BP=BC，又∵BD=BD ，∴△PBD≌△CBD（SAS），∴∠BPD=∠BCD。∵DB=DA，BC=AC，CD=CD ，∴△BCD≌△ACD ，∴∠BCD=∠ACD=12∠ACB=30° ，∴∠BPD=30°. 解：如图所示，∠BPD=30°或150°。 Hi! We are Lucy and Lily. We are sisters. We are studying in a high school. We are always wanting the weekends to come. Because on weekends there are different kinds of outdoor activities, such as going to the park, going shopping, playing ball games and so on.We usually go to the park on Saturdays. We often take some bread, meat, water and milk with us. It’s Saturday today. We are in the park again. Father is fishing in a boat on the lake(湖). Mother is sitting and reading under the tree. We are flying a kite. Now we are drinking some water. Do you think we are happy?1.Lucy and Lily are ________.A.students B.teachers C.nurses D.cousins2.What do Lucy and Lily usually do on Saturdays?A.Play ball games. B.Go to the park.C.Go for a picnic. D.Go shopping.3.How many people can we know from the passage?A.Three. B.Four. C.Five. D.Six.4.What are Lucy and Lily doing now?A.They are fishing. B.They are reading.C.They are flying a kite. D.They are drinking some water.5.Which of the following is NOT true?A.Lucy and Lily like the weekends.B.Lucy and Lily often take some food with them.C.It’s Sunday today.D.Lucy and Lily’s father is in the park, too.