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  • 实体的面、边和顶点

    lesson content

    Gayle chose migratory birds as the topic of her biology class project. She has chosen 12 pictures of different birds to display as part of her photo essay. She plans to purchase cube-shaped photo frames that allow her to place a photo on each side of the cube. How many of the photo frames does Gayle need to frame the 12 pictures? 
    ::Gayle选择迁徙鸟类作为其生物类项目的主题。 她选择了12张不同鸟类的照片作为照片论文的一部分。 她打算购买立方体形状的照片框, 让她能在立方体的每侧放置一张照片。 Gayle需要多少照片框来架设12张照片?

    In this concept, you will learn to identify the faces, edges, and  vertices  of  .
    ::在这个概念中,你会学会识别面部、边缘和顶点。

    Identifying Faces, Edges, and Vertices of Solid Figures
    ::固体数字的识别面、边缘和顶点

    A  can be defined by the number and combination of certain parts. These parts are:
    ::A可以由某些部分的数量和组合来界定。

    • Faces
      ::脸孔
    • Edges
      ::边缘
    • Vertices
      ::顶点

    These three parts are relevant to any solid that has flat surfaces, places where flat surfaces intersect and places where planes intersect.
    ::这三部分与任何具有平面的固体、平面交叉处和平面交叉处有关。

    Let’s define each part.
    ::让我们界定每一部分。

    A  face  is any flat surface. The flat surface that makes the front of this cube is called a face. Many solid figures have more than one face.
    ::面部是任何平坦的表面。 使此立方体正面的平坦表面被称为面部。 许多固态数字有一个以上的面部 。

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    An  edge  is the  line segment  where two faces meet. You can see by looking at this cube that the faces intersect in a  line . Many solid figures have more than one edge.
    ::边缘是两张脸相交的线条段。 您可以通过查看这个立方体看到, 脸部在一行中交叉。 许多固态数字有一个以上的边缘 。

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    A  vertex  is a  point  where several planes meet in a point. The arrow here is pointing to a vertex of this cube. Many solids have more than one vertex, or many  vertices .
    ::顶点是多个平面相交点的点。 箭头指向此立方体的顶点。 许多固体有多个顶点或许多顶点。

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    Let’s look at identifying the number of faces, edges and vertices of a solid figure.
    ::让我们来看看一个坚固数字的面孔、边缘和顶点的数量。

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    This is a  square   pyramid .
    ::这是平方金字塔

    The faces are the  triangle  sides and the square bottom. Given this, there are 5 faces in this pyramid.
    ::面部是三角边和平底。有鉴于此,这个金字塔里有5张脸。

    The edges are where two flat surfaces meet in a line segment. Given this, there are 8 edges in this pyramid. Edges come together at a vertex. There are five vertices in this pyramid.
    ::边缘是两个平面相交的线段。 有鉴于此, 在这个金字塔里有 8 个边缘。 边缘聚集在一个顶端 。 这个金字塔里有 5 个顶端 。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Gayle and the pictures for her photo essay.
    ::早些时候,你得到一个问题 关于盖尔 和照片的照片 她的照片作文。

    Gayle has already cropped and printed the 12 photos that will be part of biology class project. The 12 photos will be framed in cube-shaped frames. Gayle has to figure out how many frames she needs for the 12 photos. To do this, she must determine how many faces are on a cube.

    To do this, Gayle needs to first visualize a cube.
    ::Gayle已经裁剪并打印了12张照片,这些照片将成为生物类项目的一部分。 这12张照片将以立方体形状的框框设置。 Gayle必须知道12张照片需要多少个框架。 要做到这一点,她必须确定立方体上有多少面孔。 要做到这一点, Gayle需要先想象一个立方体。

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    Next, Gayle can use the definition of a cube to determine how many faces or flat planes there are or she can count the planes herself.
    ::接下来,盖尔可以使用立方体的定义 来决定有多少面孔或平面 或者她可以自己数数飞机

    A cube is a special case of a  rectangular prism , which means it has two  congruent  flat bases and four flat planes or faces. This means there are a total of 6 flat planes in a cube.
    ::立方体是一个矩形棱柱的特殊情况, 这意味着它有两个相近的平面基体和四个平面或脸。 这意味着一个立方体共有6个平面。

    12 divided by 6 is 2.
    ::12除以6等于2。

    The answer is Gayle needs 2 photo cubes to display the 12 photos.
    ::答案是 Gayle 需要两张照片来显示这12张照片。

    Example 2
    ::例2

    Answer the following question about the solid figure below.
    ::回答以下关于以下可靠数字的问题。

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    How many edges, faces and vertices are there in this figure?
    ::这个图中有多少边缘、面孔和脊椎?

    First, count the edges, which will be line segments.
    ::首先,计数边缘, 这将是线条段 。

    There are 8 line segments, so there are 8 edges.
    ::有8个线段,所以有8个边缘。

    Next, count the faces, which will be flat surfaces or flat planes.
    ::接下来,计数面,即平面或平面。

    There are 5 flat planes, so there are 5 faces.
    ::有5架平面飞机 所以有5张脸

    Then, count the vertices, which are points or corners where several edges or faces meet.
    ::然后,数数这些顶点, 也就是几个边缘或面孔相交的点或角。

    There 5 points, so there are 5 vertices.
    ::有5点,所以有5个顶点。

    The answer is, there are five vertices, five faces and eight edges.
    ::答案是,有5个顶峰,5个面孔和8个边缘。

    Example 3
    ::例3

    What are the points on a solid figure called?
    ::可靠数字上所谓的要点是什么?

    First, recall that points are the places where more than two faces meet.
    ::首先,要记住,这是两个以上面孔相遇的地方。

    The answer is vertices.
    ::答案是脊椎。

    Example 4
    ::例4

    What is the place where two faces meet called?
    ::两面相遇的地方叫什么?

    First, recall that when two faces meet, they form a line segment.
    ::首先,要记住,当两个面孔相遇时,它们就形成一个线段。

    The answer is an edge.
    ::答案是边缘。

    Example 5
    ::例5

    What are the flat sides of a figure called?
    ::数字的平面是什么?

    First, recall that the flat sides are also called flat planes.
    ::首先,回顾平面也称为平面飞机。

    The answer is faces.

    ::答案是面孔。

    Review
    ::回顾

    Identify the part of each solid indicated by the arrow.
    ::标明箭头标明的每块固体的部分。

    1. lesson content

      ::[表8]
    2. lesson content

      ::[图9]
    3. lesson content

      ::[图10]

    Answer each of the following questions about the parts of a solid figure.
    ::回答以下每一个关于一个扎实数字部分的问题。

    1. Define face.
      ::定义面部。
    2. Define edge.
      ::定义边缘 。
    3. Define vertex.
      ::定义顶点 。
    4. How many edges in a cube?
      ::立方体有多少边缘?
    5. Which plane figures make up the faces of a square pyramid?
      ::平方金字塔的面部 由哪架飞机构成?
    6. Which plane figures make up the faces of a rectangular prism?
      ::哪些平面数字构成长方形棱镜的面部?
    7. How many vertices are there in a triangular pyramid?
      ::三角金字塔里有多少顶峰?

    Identify each figure.
    ::确定每个数字。

    1. lesson content

      ::[表11]
    2. lesson content

      ::[图12]
    3. lesson content

      ::[图13]
    4. lesson content

      ::[表14]
    5. lesson content

      ::[图15]

    Review (Answers) 
    ::回顾(答复)