Section outline

  • lesson content

    Donyell walks from his house to his school. Then, after school he walks to his friend's house. He notices that his journey forms an  angle . He decides to name the angle. Donyell labels his house as point   H  , his school as  point   S  and his friend's house as point  F . Can you use the points to name of the angle formed by his journey?
    ::Donyell从他家走到他的学校,然后放学后走到他朋友家,他注意到他的旅程形成一个角度,他决定给角度命名,Donyell将他的家标为H点,将他的学校标为S点,将他朋友家标为F点。你能用这些点来命名他的旅程形成的角度吗?

    In this concept, you will learn about the parts of an angle.

    ::在这个概念中,你会了解角度的部位。

    Identifying Angles by Vertex and Ray
    ::通过 Vertex 和 Ray 识别角

    An  angle  is one of the key geometric figures that you will be working with in geometry. An angle is created when two rays connect at a common point.
    ::一个角度是您在几何学中要使用的关键几何数字之一。 当两个射线在一个共同点连接时, 一个角度会被创建 。

    lesson content

    You can see that the two rays are connected at a common  endpoint , called a  vertex . This forms the angle. An angle is named by points on the rays.
    ::您可以看到两个射线连接在一个共同的端点上,称为顶点。它形成角度。一个角度由射线上的点点命名。

    Let's look at an example of an angle.
    ::让我们看看一个角度的例子。

    lesson content

    This is angle  A B C . The vertex  B  is always in the middle. The symbol for angle looks like a small angle. 
    ::这是角度 A B C 。 顶点 B 总是在中间。 角的符号看起来像小角度 。

    A B C
    ::* A B C

    Angle  A B C  is named with this symbol.
    ::角度 A B C 以此符号命名 。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Donyell and his walk to school and then to his friend's house.
    ::早些时候,你遇到了一个问题 关于唐耶尔 和他的步行上学,然后他的朋友的房子。

    Name the angle if his house is point  H , his school is point  S  and his friend's house is point  F .
    ::若他家是H点, 他的学校是S点, 他朋友家是F点,

    First, determine the common endpoint.
    ::首先,确定共同的终点。

      S
    ::S S 级

    Then, name the angle.
    ::然后,请说出角度。

      H S F
    ::* HH S F

    The answer is  H S F .
    ::答案是"H S F"

    Example 2
    ::例2

    What is the common endpoint of the rays that form  H I J ?
    ::形成“H I J”的射线的常见端点是什么?

    First, determine the name of the common endpoint.
    ::首先,确定共同终点的名称。

    The vertex
    ::顶点

    Next, identify the location of the vertex in the angle name.
    ::下一步,在角度名称中指定顶点的位置。

    The middle point
    ::中点

    Then, write the point. 
    ::那么写点。

    I
    ::一一

    The answer is  I . The common endpoint of the rays that form  H I J  is  I .
    ::答案是我。光线中常见的终点就是我。

    Example 3
    ::例3

    Name this angle. Be sure that the vertex is in the middle.
    ::命名此角度。 请确定顶点在中间 。

    lesson content

    First, locate the common endpoint.
    ::首先,找到共同的终点。

      E
    ::英 英 英

    Then, name the angle.
    ::然后,请说出角度。

      D E F
    ::____________________________________________________________________________________________________________________________________________

    The answer is    D E F .
    ::答案是“D E F”。

    Example 4
    ::例4

    lesson content

    First, locate the common endpoint.
    ::首先,找到共同的终点。

      M
    ::M 男

    Then, name the angle.
    ::然后,请说出角度。

      L M N
    ::* L M N

    The answer is  L M N
    ::答案是"L M N"

    Example 5
    ::例5

    What is the common endpoint of the rays that form  Q R S ?
    ::构成QR S的射线的常见端点是什么?

    First, determine the name of the common endpoint.
    ::首先,确定共同终点的名称。

    The vertex
    ::顶点

    Next, identify the location of the vertex in the angle name.
    ::下一步,在角度名称中指定顶点的位置。

    The middle point
    ::中点

    Then, write the point.
    ::那么写点。

      R
    ::R R

    The answer is  R . The common endpoint of the rays that form  Q R S  is  R .

    ::答案是R。构成QR S的射线的共同终点是R。

    Review
    ::回顾

    Draw a picture to illustrate each of the named geometric figures.
    ::绘制图片以说明每个命名的几何数字。

    1. A B
      ::A B ______________________________________________________________________________________________________________________________________________________________________________________
    2. C D
      ::C D __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
    3. D E
      ::D E ______________________________________________________________________________________________________________________________________________________________________________________________________________________
    4. A B C
      ::* A B C
    5. L M N
      ::* L M N
    6. X Y ¯
      ::# 你 # # X Y #
    7. P Q
      ::PQ____________________________________________________________________________________________________________________________________
    8. G H
      ::G H _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
    9. A B D E
      ::A B D E
    10. L M D E
      ::L M D E
    11. R S T U
      ::R S
    12. D F ¯ X Y ¯
      ::# 达芙 # * X Y #

    Define the following terms.
    ::界定以下术语。

    1. Ray
      ::雷
    2. Line
      ::线线线
    3. Vertex
      ::顶点
    4. Line Segment
      ::行线段段

    Review (Answers) 
    ::回顾(答复)