The students from Xinjiang enjoy staying in our school because everyone is        to them.

He is       and he has an     sister.

—What          news it was!—Yes, all of the children were very            .

—Do you think yesterday’s math problem was difficult?—Yes. I could         work it out.

如图,在同一平面内将两个全等的等腰Rt△ABC和△ADE摆放在一起,A为公共顶点,∠BAC=∠AED=90°,若△ABC固定不动,△ADE绕点A旋转,AD,AE与边BC的交点分别为F,G(点F不与点B重合,点G不与点C重合).若BG=8,AB=,CF=9,则AG=      ,AF=       .()

如图,在同一平面内将两个全等的等腰Rt△ABC和△AFG摆放在一起,A为公共顶点,∠BAC=∠AGF=90°,若△ABC固定不动,△AFG绕点A旋转,AF,AG与边BC的交点分别为D,E(点D不与点B重合,点E不与点C重合).若BD=4,DE=5,CE=3,则AD=      ,AE=       .()

如图,在同一平面内将两个全等的等腰Rt△ABC和△AFG摆放在一起,A为公共顶点,∠BAC=∠AGF=90°,若△ABC固定不动,△AFG绕点A旋转,AF,AG与边BC的交点分别为D,E(点D不与点B重合,点E不与点C重合).AB=2,BE=m,CD=n,求m,n满足的关系式为()

如图,在矩形ABCD中,AD=4,AB=10,点P是AB边上的任意一点(不与A,B重合),连接PD,过点P作PQ⊥PD,交直线BC于点Q.若点Q与点C重合,则AP=________________.

如图,四边形ABCD是等腰梯形,AD∥BC,AB=4,BC=9,P为BC边上一动点(不与点B,C重合),连接AP,过点P作PE交CD于点E,使得∠APE=∠ABC.则当BP=___________时,点E为CD的中点.

如图,直角梯形ABCD中,AD∥BC,∠B=90°,AD=1,BC=8,AB=6,点P在高AB上滑动,当AP长为_________时,△DAP与△PBC相似.