9.10四边形分类

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  四边形分类

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  [Figure 1]

  
  ::[图1]

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  David is cutting out shapes in art class. He cuts a variety of shapes. One of the shapes that he cuts out has  opposite  sides that are  congruent  and four 90 degree  angles . He notices that one pair of opposite sides is longer than the other pair of opposite sides. What type of shape did David cut out?
  ::大卫在艺术类中切除形状。 他切开各种形状。 他切开的形状之一的两面相同,四面90度角。 他注意到一对对相反的形状比另一对的长。 大卫切开的形状是哪种?

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  In this concept, you will learn about quadrilaterals.
  
  ::在这个概念中,你会了解四边形。

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  Classifying Quadrilaterals
  ::分类四边债

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  A  quadrilateral  is a closed figure with four sides and four  vertices . The  vertex  is a  point  where  line  segments meet. The points where the sides of a quadrilateral meet are called the vertices (which is the plural form of "vertex"). The prefix “quad” means four. You can always remember that a quadrilateral is a four sided figure because of this prefix.
  ::四边形是一个有四面和四个顶点的封闭形。顶点是线段相交点。四边形相交点被称为顶点(这是“顶点”的多元形式)。前缀“方形”是指四。您可以记住,四边形因此前缀而是一个四边形。

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  Each quadrilateral has four sides and four angles.
  ::每个四边形都有四面四角和四个角度

  

  [Figure 2]

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  A quadrilateral has four angles. You can name the angles by using the angle symbol and the letter of each vertex. This figure is  $\begin{array}{r}\mathrm{\angle }A,\mathrm{\angle }B,\mathrm{\angle }C,\mathrm{\angle }D\end{array}$ .
  ::四边形有四个角度。 您可以使用角度符号和每个顶点的字母来命名角度。 此数字是 A, B, C, D 。

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  A quadrilateral has four vertices. They are named by the letters,  $\begin{array}{r}A,B,C\end{array}$  and  $\begin{array}{r}D\end{array}$ . Naming the quadrilateral uses a small quadrilateral symbol and the four letters of the vertices,  $\begin{array}{r}◻ABCD\end{array}$ .
  ::一个四边形有四个顶点。它们的名字是字母A、B、C和D。四边形的名称使用一个小四边形符号和四边形的字母“A B C D”。

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  A quadrilateral has four sides. The sides are named by the endpoints of each  line segment . The sides are  $\begin{array}{r}\overline{AB},\overline{BD},\overline{CD},\overline{AC}\end{array}$ .
  ::四边有四边,两边由每条线段的终点命名。两边是 A B 、 B D 、 C D 、 A C 。

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  There are several different kinds of quadrilaterals. Quadrilaterals are classified and identified based on angles and side lengths. While each four sided figure is a quadrilateral, sometimes there is a name that is more specific.
  ::有几种不同的四边形。四边形根据角度和侧边长度进行分类和识别。每四个边形图是一个四边形,有时有一个更具体的名称。

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  A   is a quadrilateral with opposite sides that are  parallel  and  congruent . Congruent  means exactly the same. In this case, a parallelogram has opposite sides that are parallel and congruent meaning that they have the same length.
  ::A 是两面平行的四边形。 Congruent 的意思完全相同。 在此情况下, 平行图的两边是平行的、 一致的, 意思是相同的长度 。

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  Here is a parallelogram.
  ::这里有一个平行图。

  

  [Figure 3]

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  Notice that the opposite angles in this parallelogram are the same. In this figure, one pair of angles is acute and one pair of angles is obtuse. The arrows indicate the obtuse angles. The other two angles are acute. This is sometimes true but not always. Let’s look at a  rectangle .
  ::请注意, 这个平行图中的相反角度是相同的。 在这个图中, 一对角度是急性的, 一对角度是模糊的。 箭头显示的是斜角。 另外两个角度是急性的。 这有时是真实的, 但并不总是如此。 让我们看看矩形 。

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  A  rectangle  is a parallelogram with four right angles. This means that a rectangle has opposite sides parallel and congruent and it also has four right angles.
  ::矩形是一个具有四个右角度的平行图。 这意味着矩形的对面平行和相近, 并有四个右角度 。

  

  [Figure 4]

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  A  square  is a rectangle with four congruent sides and four right angles. Notice that the properties of a parallelogram applies to squares, too.
  ::一个正方形是一个矩形,有四个相容的侧面和四个右角度。请注意,平行图的属性也适用于正方形。

   

  

  [Figure 5]

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  A  rhombus  is a parallelogram with four congruent sides. Notice that a rhombus does not ALWAYS have right angles like a square, but it does always have congruent sides.
  ::暴风车是一个平行图,有四个相似的两面。 注意暴风车没有像广场那样的正确角度,但它总是有一致的一面。

  

  [Figure 6]

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  A  trapezoid  is a parallelogram with one pair of opposite sides parallel. Here is an example of a trapezoid.
  ::形图是一个平行图,一对对面平行。这里是形图的一个实例。

  

  [Figure 7]

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  Notice that this trapezoid has two  acute angles  and two obtuse angles. Be sure to check out the angles when you look at a trapezoid.
  ::请注意, 此类有两个急性角度和两个模糊角度 。 当您看到类时, 请务必检查角 。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about David and his shapes.
  ::之前,你被问及大卫和他的形状

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  One of his shapes has two pairs of parallel sides that are congruent, four 90 degree angles and one pair of opposite sides is longer than the other pair. What type of shape did David cut out?
  ::他的一个形状有两对平行的两面,两边是相同的,四90度角和一对对对对的两边比另一对长。 大卫切掉了哪种形状?

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  First, note if any of the sides are the same length.
  ::首先,如果双方的长度相同,请指出。

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  Yes, opposite sides are the same length.
  ::是的,对立面的长度相同。

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  Next, determine if there are any right angles.
  ::下一位,确定是否有右角度

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  Yes, all four angles
  ::是的,所有四个角度

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  Then, classify the shape.
  ::然后,分类形状。

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  Rectangle
  ::矩形

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  The answer is a rectangle.
  ::答案是一个矩形。

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  Example 2
  ::例2

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  What is the name of the figure?
  ::数字叫什么名字?

  

  [Figure 8]

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  First, look to see if any of the sides are the same length.
  ::首先,看看是否有双方的长度相同。

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  Yes, all four sides
  ::是,四面四方

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  Next, look to see if there are any right angles.
  ::下一位,看看有没有正确的角度

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  Yes, all four angles
  ::是的,所有四个角度

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  Then, classify the shape.
  ::然后,分类形状。

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  Square
  ::广场广场

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  The answer is a square.
  ::答案是方形的。

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  Example 3
  ::例3

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  Identify the following quadrilateral. Be as specific as you can.
  ::识别以下四边形。尽可能具体。

  

  [Figure 9]

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  First, look to see if any of the sides are the same length.
  ::首先,看看是否有双方的长度相同。

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  Yes, all four sides
  ::是,四面四方

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  Next, look to see if there are any right angles.
  ::下一位,看看有没有正确的角度

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  Yes, all four angles
  ::是的,所有四个角度

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  Then, classify the shape.
  ::然后,分类形状。

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  Square
  ::广场广场

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  The answer is a square.
  ::答案是方形的。

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  Example 4
  ::例4

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  Identify the following quadrilateral. Be as specific as you can.
  ::识别以下四边形。尽可能具体。

  

  [Figure 10]

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  First, look to see if any of the sides are the same length.
  ::首先,看看是否有双方的长度相同。

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  No
  ::否 无

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  Next, count the pairs of parallel sides.
  ::接下来,计数平行的两边。

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  One
  ::一个

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  Then, classify the shape.
  ::然后,分类形状。

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  Trapezoid
  ::细胞类

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  The answer is a trapezoid.
  ::答案是一个陷阱状的。

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  Example 5
  ::例5

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  Identify the following quadrilateral. Be as specific as you can.
  ::识别以下四边形。尽可能具体。

  

  [Figure 11]

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  First, look to see if any of the sides are the same length.
  ::首先,看看是否有双方的长度相同。

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  Yes, the opposite sides
  ::是的,对立的两面

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  Next, look to see if there are any right angles.
  ::下一位,看看有没有正确的角度

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  No
  ::否 无

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  Then, classify the shape.
  ::然后,分类形状。

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  Parallelogram
  ::平行图

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  The answer is a parallelogram.
  
  ::答案是一个平行图。

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  Review
  ::回顾

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  Look at each image and name the quadrilateral pictured.
  ::看看每张图像 并命名四边图片。

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  1. 

     [Figure 12]
     
     ::[图12]
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  2. 

     [Figure 13]
     
     ::[图13]
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  3. 

     [Figure 14]
     
     ::[表14]
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  4. 

     [Figure 15]
     
     ::[图15]
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  5. 

     [Figure 16]
     
     ::[图16]

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  Name the geometric figure described below or answer each question.
  ::说明以下几何数字或回答每个问题。

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  6. Has four sides and four angles
     ::有四面四角度
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  7. Has one pair of opposite sides that are parallel
     ::有一对对对对立的对立面是平行的
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  8. Has four right angles and four congruent sides
     ::4个右角度和4个相近的侧面
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  9. A parallelogram with four right angles.
     ::具有四个右角度的平行图。
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  10. A parallelogram with four congruent sides
      ::具有四个一致面的平行图
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  11. Has four right angles
      ::四个右角度
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  12. Has four sides
      ::有四面四面
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  13. The word "parallel is part of it's name
      ::"平行是它名字的一部分"
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  14. True or false. A parallelogram is also a square.
      ::真实的或假的。平行图也是正方形 。
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  15. True or false. A square is also a rectangle.
      ::不管是真还是假,方形也是矩形

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源