22.3（4） 正方形 Square

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1、22.3（4） 正方形 Square教学目的：理解正方形的概念，知道它与矩形、菱形、平行四边形之间的内在联系，掌握正方形的特殊性质与判定方法，并能运用这些知识进行有关的证明和计算。Teaching aim: To get the students to understand the concept of a square, to know its intrinsic connection with rectangles, diamonds, and parallelograms, to grasp the special properties and determination methods

2、 of a square, and to be able to use these knowledge to perform relevant proofs.教学重点：1、理解正方形的定义，知道它与平行四边形、矩形、菱形的联系；2、掌握正方形的性质及其基本运用。Key points : 1. Understand the definition of a square and know its connection with parallelograms, rectangles, and diamonds;2. Master the properties of a square and its

3、basic application.教学难点：运用正方形的性质解决问题。Teaching difficulties: Using the nature of the square to solve problems.教学过程：Teaching Process:一、 复习引入Review and Introduction矩形rectangle四边形quadrilateral平行四边形Parallel quadrangles正方形square菱形rhombus二、 正方形的定义和判定 The Definition and Determination of Square1、 正方形的定义：The D

4、efinition of the Square有一组邻边相等并且有一个内角是直角的平行四边形叫做正方形。A set of parallelograms with equal neighboring sides and an inner angle is a right angle is called a square.2、实验操作：An Experimental Operation将长方形纸片裁成正方形纸片Cut rectangular pieces of paper into square pieces.3、正方形的判定：Determination of Square正方形的性质判定1：有一

5、组邻边相等的矩形是正方形。1、There is a set of squares with equal neighboring sides.正方形的性质判定2：有一个内角是直角的菱形是正方形。2、A diamond with a right angle is a square.4、概念辨析：Conceptual Analysis下列四边形是不是正方形？Determine if the following graphics are squares：（1）对角线相等的菱形 Diagonally equal diamond.（2）对角线互相垂直的矩形 A rectangle perpendicula

6、r to each other.（3）对角线相等且垂直的平行四边形An equal and vertical parallelogram of diagonal lines.（4）对角线相等且垂直且互相平分的四边形A quad that is equal and vertical and equally divided on the diagonal.小结：对角线_的矩形是正方形，对角线_的菱形是正方形，对角线_的平行四边形是正方形，对角线_的四边形是正方形三、正方形的性质 The Properties of a Square1、正方形的性质：正方形的性质1：正方形的四个角都是直角，四条边都相

7、等。The four corners of the square are all right angles, and all four sides are equal.正方形的性质2：正方形的对角线相等且互相垂直平分，每条对角线平分一组对角。The diagonal lines of the square are equal and equally divided vertically with each diagonal equally divided a set of diagonals.正方形是一个是中心对称图形，也是轴对称图形。A square is a center symmetry

8、 graphic and an axisymmetric graphic.3、正方形性质的应用Application of Square Properties（1）简单应用：Simple Application 根据图形求出相应的x、y的值：Find the corresponding X, Y values according to the graph.（2）例题讲解 Examples如图，已知正方形ABCD中，F在边AB上的，将FBC沿CF翻折，若点B恰好落在对角线AC上，求FB的长。As shown in the figure, in the known square ABCD, F i

9、s on side AB, the FBC is folded along the CF. If point B happens to fall on the diagonal AC, find the length of the FB.变式：将条件中F点沿AB移动，使得FCB=15延长CF和对角线DB使之交于点P，求证：APC是等边三角形Variation: Move point F along AB so that FCB = 15 . Extend CF and DB to make it intersect at point P, find out: APC is an equilat

10、eral triangle.（3）思维拓展：Thinking Development如图，正方形ABCD中，M在线段BC上，N在线段CD上，且MAN=45，求证：MN=DN+BM. As shown in the square ABCD, M is on the line segment BC, N is on the line segment CD, andMAN = 45 , verify: MN = DN + BM拓展：将问题中的“M在线段BC上，N在线段CD上，”改成“M在直线BC上，N在直线CD上，”讨论结果会有什么变化。. Expand: Replace M is on the l

11、ine segment BC, N is on the line segment CD, with M is on the line BC, N is on the line CD, what will happen?三、 小结与作业 Summary and assignments1、 小结：正方形的定义、判定和性质Summary: The Definition, Decision, and Nature of a Square2、 作业：Assignments（1） 完成练习册22.3（4）Complete Exercise book 22.3(4)（2） 思考拓展题 Finish “further thinking II”（3） 整理特殊平行四边形的知识结构Go over the structure of special parallelograms.