视线遮挡问题教学设计范文

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate corresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和九年级数学《相似三角形的遮挡问题》教学设计. 一、教学目标

知识与技能

.进一步巩固相似三角形的知识，发展学生综合运用相似三角形的判定方法和性质解决问题的能力，提高学生的数学应用意识，加深对相似三角形的理解与认识．

过程与方法

.能够运用三角形相似的知识解决不能直接测量物体的长度和高度

情感态度与价值观

.通过把实际问题转化成有关相似三角形的数学模型

二、重点难点

重点

在实际问题中，构造相似三角形的模型以及运用相似形的知识解决问题．

利用工具构造相似三角形的模型．

难点 三、学情分析

用相似三角形解决实际问题，在我们的现实生活中有着重要的应用，它能解决人们不能直接测量的问题。

四、教学过程设计

情境创设

一．判断两个三角形相似有哪些方法？

1.

定义

2.定理（平行法）

2.

判定定理一（边边边）

3.

判定定理二（边角边）

4.

判定定理三（角角）

二．相似三角形有什么性质？

给出图片世界上最高的树、高楼、河的图片。

教师提出问题

提高学生的学习兴趣，激发学生的求知欲望，从而引出本节课题

问题一：利用阳光下的影子．测量金字塔的高度

操作：在金字塔影子的顶部立一根本杆，借助太阳光线构成两个相似三角形，来测量金字塔的高度。如果木杆EF长2m，它的影长FD为3 m，测得OA为201 m，求金字塔的高度BO.

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate corresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和

(1)太阳光线BA、ED之间有什么关系？

(2)△ABO和△DEF有什么特殊关系？

(3)

由EF=2m，FD=3m，OA=201m，怎样求BO？

一题多解 还可以有其他方法测量吗？

△ABO∽△AEF

教师提出问题. 学生读题，并理解测量方案. 进行抢答问题

怎样测量旗杆的高度? 提出：在阳光下，在同一时刻，物体的高度与物体的影长存在某种关系：物体的高度越高，物体的影长就越长

在平行光线的照射下，不同物体的物高与影长成比例

2

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate ped, acorresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shand round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和 知识要点1（测高的方法）

测量不能到达顶部的物体的高度，通常用“在同一时刻物高与影长成正比例”的原理解决。 物1高

：物2高 = 影1长

：影2长

跟踪训练

在同一时刻物体的高度与它的影长成正比例，在某一时刻，有人测得一高为1.8米的竹竿的影长为3米，某一高楼的影长为60米，那么高楼的高度是多少米？

解:设高楼的高度为x米，则

1.8x360601.8x3x36

问题二：估算河的宽度

方案：选择目标点。测量相关数据．如图，在河对岸选定一个目标点P，在近岸取点Q和S，使点P，Q，S共线且直线PS与河垂直，接着在过点S且与PS垂直的直线a上选择适当的点T，确定PT与过点Q且垂直PS的直线b的交点R，如果测得QS=45 m。ST=90 m，QR=60 m，求河的宽度PQ．

P

Q S R b T a 第

3

页

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate corresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和知识要点2（测距的方法）

测量不能到达两点间的距离,常构造相似三角形求解。 跟踪训练

为了估算河的宽度，我们可以在河对岸选定一个目标作为点A，再在河的这一边选点B和C，使AB⊥BC，然后，再选点E，使EC⊥BC，用视线确定BC和AE的交点D．此时如果测得BD＝120米，DC＝60米，EC＝50米，求两岸间的大致距离AB．

问题三：利用标杆，形成盲区

已知左、右并排的两棵大树的高

分别是AB=8m和CD=12m，两树的根

部的距离BD=5m。一个身高1.6m的人

沿着正对这两棵树的一条水平直路l从左向右前进，当他与左边较低的树的距离小于多少时，就不能看到右边较高的树的顶点C？

ACBDE

分析：

假设观察者从左向右走到点E时，他的眼睛的位置点F与两颗树的顶端点A、C恰在一条直线上,如果观察者继续前进，由于这棵树的遮挡，右边树的顶端点C在观察者的盲区之内，观察者看不到它。（例题讲解）

4

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate ped, acorresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shand round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和

跟踪训练

1、如图,铁道口的栏杆短臂长1m,长臂长16m,当短臂端点下降0.5m时,长臂端点升高 多少m。 测量树高

(1) 小明测得长为1米的竹竿影长为0.9米，同时，小李测得一棵树的影长为5.4米，请计算小明测量这棵树的高; (2)同时小王在测另一棵树时，发现树影的一部分在地面上，而另一部分在墙上，他测得地面上的影长为2.7米，留在墙上部分的影长为1.2米.请计算小王测量的这棵树的高.

(3) 小明﹑小李二位同学再想利用树影测量树高. 小明测得长为1米的竹竿影长为2米，同时，小李测量一棵树时发现树影的一部分在地面上，另一部分在斜坡的坡面上，测得在地面影长为10米，在斜坡上影长为4米，斜坡的倾斜角为30°，请计算这棵树的高

开发学生发散思维进行一题多解

练习：、

1、小明把手臂水平向前伸直，手持长为EF的小尺竖直，瞄准小尺的两端E、F，不断调整站立的位置，使站在点D处正好能看到旗杆的顶部和底部，如果小明的手臂长 =40㎝，小尺长EF=20㎝，点D到旗杆底部的距离AD=40m，求旗杆的高度。

第

5

页

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview ascores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units "1") (2) find associate "volume rate corresponds to" relationship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and toolmeasurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and nswers parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和2.如图，一条河的两岸有一段是平行的，在河的南岸边每隔5米有一棵树，在北岸边每隔50米有一根电线杆．小丽站在离南岸边15米的点处看北岸，发现北岸相邻的两根电线杆恰好被南岸的两棵树遮住，并且在这两棵树之间还有三棵树，则河宽为

米．

3.

为了测量路灯（OS）的高度,把一根长1.5米的竹竿（AB）竖直立在水平地面上,测得竹竿的影子（BC）长为1米,然后拿竹竿向远离路灯方向走了4米（BB‘）,再把竹竿竖立在地面上, 测得竹竿的影长（B‘C‘）为1.8米,求路灯离地面的高度

ShOABCA'B'C'

课堂小结:

一

、相似三角形的应用主要有如下两个方面

1 测高(不能直接使用皮尺或刻度尺量的) 2 测距(不能直接测量的两点间的距离) 二、测高的方法

测量不能到达顶部的物体的高度,通常用“在同一时刻物高与影长的比例”的原理解决 三、测距的方法

测量不能到达两点间的距离,常构造相似三角形求解

6