题目

在矩形ABCD中，AD＝6，AB＝2 ，点E是边AD上的一个动点，连接BE，以BE为一边在其左上方作矩形BEFG，过点F作直线AD的垂线，垂足为点H，连接DF. （1） 当BE＝EF时.①求证：FH＝AE；②当△DEF的面积是 时，求线段DE的长； （2） 如图2，当BE＝ EF，且射线FE经过CD的中点时，请直接写出线段FH长. 答案：解：①∵FH⊥AE， ∴∠FEH+∠HFE＝90°， ∵矩形BEFG， ∴∠FEH+∠AEB＝90°， ∴∠AEB＝∠HFE， 在△FHE与△EAB中， {∠BAE=∠EHF=90∘∠HFE=∠AEBBE=EF ， ∴△FHE≌△EAB（AAS）， ∴FH＝AE； ②∵△FHE≌△EAB， ∴AE＝FH， ∵AD＝6， 设CD＝x，AE＝6﹣x， ∵△DEF的面积＝ 358=12DE⋅FH ， 可得： 12×(6−x)=358 ， 解得： x1=52,x2=72 Bruce Carter went to his office and he found a note(便条) on his desk. Read it and find out more information. 【1】Who is probably(可能) ill?A. Bruce Carter B. Bruce Carter’s sonC. The dog D. Bruce Carter’s daughter【2】Where did Bruce find the note?A. At home. B. In his office. C. In the hospital. D. We don’t know.【3】Which of the following is True according to the note?A. Mrs. Carter called Mr. Carter at 4:30 p.m. B. Jerry is Mr. Carter’s son. C. Mr. Carter should go to bed before 10:00 p.m. D. Mr. Carter was out when Mrs. Carter called.【4】Who’s Jerry?A . Bruce Carter’s friend. B. Bruce Carter’s secretary. C. Bruce Carter’s wife. D. A nurse in the hospital.【5】According to(根据)the note, what should Mr. Carter do?A. Call Mrs. Carter. B. Give the dog food. C. Stay in hospital. D. Take Judy out for dinner.