问题 证明题

如图,以Rt△ABC的直角边AC. BC向形外作正方形ACGH. 正方形CBEF,连结GE. AE

求证:(1)AE=GE;(2)EC垂直平分AG。

答案
证明:(1)连结CE ∵四边形ACGH、CBEF是正方形
∴AC=CG,∠CFE=∠BCF=45°
∵∠ACB=∠QCF=90°∴∠ACE=∠GCE
∵CE=CE   ∴△ACE≌△GCE
∴AE=GE
(2)∵AC=CG,AE=GE
∴C、E都在线段AG的中垂线上 ∴CE垂直平分AG
单项选择题
问答题

Passage 2 For the past two decades, I have worked in consultation with administrators and teachers in hundreds of schools that are committed to school-wide reform. Using an approach known as the Responsive Classroom model, these schools are working to improve the quality of education by making significant changes in the way time is structured and used. This model allows more time for relationships, in-depth research, inquiry and reflection. Schools commit a minimum of three years to implement the Responsive Classroom model. Below are some of the key systemic changes that this model advocates. // 1.Allow time for in-depth learning, investigation and contemplation by narrowing the scope of the curriculum and lengthening time blocks. The answer to meeting each day’s curriculum expectations is found in a paradox. We must consider smaller topics for longer periods of time in order to accomplish more. This can be clearly seen at the middle school level, where recent research findings have made it evident that block scheduling, small classes and "advisory" periods improve student behavior and academic performance. // 2.Begin the school year slowly: Encourage teachers to take time to set clear social and academic expectations and to establish an atmosphere of trust. Instruction cannot be delivered in classrooms where children are unfocused, inattentive and struggling with one another. Teachers must know how to create a trustworthy space for learning before learning can occur. //During the first six weeks, teachers set goals, generate rules with students and guide students’ discoveries of new materials, equipment and supplies. They take time to build trust so students will take risks, ask questions and state their ideas. In the long run both teachers and students gain time by taking time. Discipline problems are fewer and less time-consuming than in classrooms where the social expectations are not clear. Children better understand academic expectations, and academic outcomes improve. // 3.Allow time for reflection and review throughout the year. Periods following vacations require review of social and academic expectations. Taking the time for this reexamination of basic expectations will create more time for learning. During the last six weeks of school, students should reflect on their year in order to see all they have accomplished. // 4.Adjust the schedule of the school day to change the nature and productivity of the afternoon. In the middle of the day the children need a break from the rigor of academics. Many schools use a midday schedule that gives children recess, followed by lunch and then quiet time. This break helps children to be productive and engaged in the afternoon. The idea of a quiet time after lunch may be unthinkable to many teachers, given all they believe they must fit into the day, but here, again, is a paradox of teaching and learning: Quiet time away from academic demands increases learning. // 5.Change the school schedule to allow more time for teachers, staff, administration and parents to interact with one another. Devising schedules that allow time for grade-level and team planning is an important administrative function. Administrators should schedule the first parent// teacher conference as close to the beginning of the year as possible. By asking parents what they would like their children to learn in school this year, a partnership between home and school can be created before problems have a chance to arise. Teachers also can use this conference to share goals, learn about their students and share their expectations. // If we truly wish to transform our schools into challenging, exciting and secure places, we need an education system that is dedicated, from top to bottom, to giving teachers more time to teach and children more time to learn. //