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  • 规则多边形和不规则多边形分类

    lesson content

    ::[图1]

    Arletta's teacher wants the class to identify regular and irregular polygons in the classroom. Arletta missed the previous day of class when her teacher discussed the definitions of regular and irregular polygons. Arletta measures her desk and finds that the side lengths are different. She turns to her classmate and asks if she should classify the  polygon  as regular or irregular. What should her classmate tell her to write as the classification of the polygon?
    ::Arletta的老师想让班级识别课堂上的常规和非常规多边形。 Arletta在上课的前一天错过了班里老师讨论常规和非常规多边形定义的前一天。 Arletta测量了课桌,发现侧边长度不同。 她向同学求助,询问她是否应该将多边形归类为常规或非常规。 她的同学应该告诉她写什么作为多边形的分类?

    In this concept, you will learn to identify regular and irregular polygons.

    ::在此概念中,您将学会识别常规和非常规多边形。

    Classifying Regular and Irregular Polygons
    ::正规和非正规多边形分类

    All polygons can be classified as  regular  or  irregular  polygons.
    ::所有多边形均可归类为常规或非常规多边形。

    A  regular polygon  is an equilateral polygon where all the side lengths are  congruent , and an equiangular polygon where all the  angles  are congruent.
    ::普通多边形是指所有侧长均匀的等边多边形,以及所有角度均匀的等角多边形。

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    This  triangle  is a regular polygon. All three side lengths are congruent and all three angles are congruent. Here is an example of an  irregular polygon .
    ::此三角形是一个普通多边形。 所有三个侧边长度都是相容的, 所有三个角度都是相容的。 下面是非常规多边形的例子 。

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    By counting the sides, you can see that this is a five sided figure. It is a  pentagon . However, the sides are not congruent. Therefore, it is an irregular pentagon. Irregular polygons have side lengths that are not congruent.
    ::通过计数边, 您可以看到这是一个五边形的图。 这是一个五边形的图。 但是, 双边并不一致 。 因此, 它是一个非常规的五边形。 非正统多边形的侧边长度不相同 。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Arleta and her desk.
    ::早些时候,你遇到了一个问题 关于阿莱塔和她的办公桌。

    She measured the sides of her desk and found that they were different lengths, but she doesn't know if that means that the polygon was regular or irregular. What should her classmate tell her to write as the classification of the polygon?
    ::她测量了办公桌的侧面,发现其长度不同,但她不知道这是否意味着多边形是正常的还是不正常的。 她的同学应该告诉她写什么作为多边形的分类?

    First, determine if all of the sides are congruent.
    ::首先,确定各方是否一致。

    No
    ::否 无

    Then, classify the polygon.
    ::然后对多边形进行分类。

    Irregular
    ::非正规

    The answer is an irregular polygon. Her classmate should tell her to write that it is an irregular polygon.
    ::答案是非常规多边形。她的同学应该告诉她写它是一个非常规多边形。

    Example 2
    ::例2

    Jessie measures one of her bedroom walls and finds that it is 12 feet long. She measures another wall and finds that it is 10 feet long. The other two walls are also different lengths. Is her room shaped like a regular polygon or an irregular polygon?
    ::杰西用她的卧室的墙壁测量她的卧室,发现它长12英尺。她用另一面墙壁测量,发现它长10英尺。另外两面墙的长度也不同。她的房间是像普通多边形还是非常规多边形?

    First, determine if all of the lengths are the same.
    ::首先,确定所有长度是否相同。

    No
    ::否 无

    Then, classify the polygon.
    ::然后对多边形进行分类。

    Irregular
    ::非正规

    The answer is an irregular polygon.
    ::答案是非常规多边形。

    Example 3
    ::例3

    Name the figure as a regular or irregular polygon.
    ::将图形命名为普通多边形或非常规多边形。

    lesson content

    First, look at the sides to see if they look congruent.
    ::首先,看看两边 看看他们是否看起来一致。

    Yes
    ::是 是

    Then, classify the polygon.
    ::然后对多边形进行分类。

    Regular polygon
    ::经常多边形

    The answer is a regular polygon.
    ::答案是一个常规多边形。

    Example 4
    ::例4

    Name the figure as a regular or irregular polygon.
    ::将图形命名为普通多边形或非常规多边形。

    lesson content

    First, look at the sides to see if they look congruent.
    ::首先,看看两边 看看他们是否看起来一致。

    No
    ::否 无

    Then, classify the polygon.
    ::然后对多边形进行分类。

    Irregular polygon
    ::非正非多边形

    The answer is an irregular polygon.
    ::答案是非常规多边形。

    Example 5
    ::例5

    Name the figure as a regular or irregular polygon.
    ::将图形命名为普通多边形或非常规多边形。

    An  octagon  with all sides measuring 4 centimeters.
    ::八角形,方形四厘米

    First, determine if all of the sides are congruent.
    ::首先,确定各方是否一致。

    Yes
    ::是 是

    Then, classify the polygon.
    ::然后对多边形进行分类。

    Regular polygon
    ::经常多边形

    The answer is a regular polygon.
    ::答案是一个常规多边形。

    Review
    ::回顾

    Based on each description, determine whether the polygon is regular or irregular.
    ::根据每一项说明,确定多边形是正常的还是不正常的。

    1. A quadrilateral with all sides equal to 5 cm and all right angles.
      ::方形四边形,方形等于5厘米,角度均匀。
    2. A pentagon with different side lengths.
      ::具有不同侧边长度的五边形。
    3. A square.
      ::一个广场。
    4. A rectangle.
      ::一个矩形。
    5. An octagon with one side that is 8 cm and the other sides congruent to that side. All angles are congruent.
      ::八角形,其一面为8厘米,另一面与该面相似。所有角度都是相同的。
    6. A heptagon with seven congruent sides and angles.
      ::一个七边形七角形,有七个相容的侧面和角度。
    7. A hexagon with six congruent angles.
      ::六角形六角形,六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形六角形。
    8. A hexagon with the following side lengths: 4 m, 5 m, 7 m, 5 m, 4 m and 7 m.
      ::六边形:4米、5米、7米、5米、4米和7米。
    9. A pentagon with five congruent angles.
      ::五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形,五角形。
    10. True or false. A figure can be a polygon and be regular or irregular.
      ::数字可以是多边形,可以是常规的,也可以是非常规的。

    Use the image below to answer questions 11-18. Identify the polygon below based on the number of sides it has.
    ::使用下面的图像回答问题 11-18。 根据下面的边数确定下面的多边形 。

     

    lesson content

    1. a
      ::a a/
    2. b
      ::b b b
    3. c
      ::c , c , c , c
    4. d
      ::d , d , d , d , d , d , d , d , d , d , d

    Identify if the shapes in the above image are regular or irregular.
    ::确定上述图像中的形状是正常的还是不正常的 。

    1. a
      ::a a/
    2. b
      ::b b b
    3. c
      ::c , c , c , c
    4. d
      ::d , d , d , d , d , d , d , d , d , d , d

    Review (Answers) 
    ::回顾(答复)