对称线
章节大纲
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::[图1]Raven has been studying lines of symmetry with her class. When she goes home, she looks at her cat and notices that his face is symmetrical. She grabs a sheet of paper and holds it in the middle of her cat's face, then she rotates the paper to see if the cat's face has other lines of symmetry. What type(s) of line symmetry does Raven's cat have?
::Raven一直在研究与班级的对称线。当她回家时,她看着她的猫,注意到他的脸是对称的。她拿了一张纸,放在猫的脸上,然后她转动了纸,看看猫的脸是否有其他对称线。Raven的猫有哪几条线对称?In this concept, you will learn about symmetry.
::在这个概念中,你会了解对称性。Symmetry
::对对称In geometry, a figure or an object can have symmetry . Symmetry is having one side that exactly mirrors the other.
::在几何学上,一个数字或物体可以有对称性。对称性是一面与另一面完全对应。Here is a butterfly. Notice that you can draw a line right down the center of the butterfly and one side will match the other side. Here is what that looks like.
::这是一只蝴蝶。请注意,你可以在蝴蝶中间画一条线,另一边则与另一边相匹配。这是看起来的样子。When you can divide a figure or an object into two even matching halves, you say that the figure has line symmetry .
::当您可以将一个数字或一个对象分成两个甚至匹配的二分之一时,您会说该数字具有线对称性。This figure can be divided in one way, vertically. If you tried to divide it horizontally, the two sides would not match.
::这个数字可以垂直地以一种方式分割。 如果您试图横向分割, 则双方不匹配 。Therefore, you can say that the butterfly has bilateral symmetry . Bilateral symmetry means that it has one line of symmetry that divides the butterfly in half.
::因此,你可以说蝴蝶有双边对称性。双边对称性意味着它有一条对称线,将蝴蝶分成两半。A line of symmetry is a line that splits a figure into symmetrical parts. In the butterfly, there is one line of symmetry that can be drawn to show the two equal matching halves of the butterfly.
::对称线是将数字分割成对称部分的线条。在蝴蝶中,可以画出一条对称线来显示两对等的蝴蝶半径。Let’s look at a picture of a figure that has more than one line of symmetry.
::让我们看看一个数字的图象,该图不只一行对称。Here is a cross. This cross has four lines of symmetry. You can divide it vertically and horizontally and both sides will match. That shows two lines of symmetry.
::这里有一个十字架。 这个十字架有四行对称。 您可以垂直和水平分割它, 并且两侧会匹配。 这显示了两行对称 。There are other types of symmetry. There is turn or rotational symmetry . Rotational symmetry means that you can rotate the figure around a fixed point and it will look the same.
::有其他类型的对称。 有旋转或旋转对称。 旋转对称意味着您可以在固定点周围旋转数字, 并且它看起来会是一样的 。This star has rotational symmetry. It looks exactly the same no matter which point is rotated to be at the top. Since there are 5 points, this is a figure with a rotational symmetry of 5.
::这个恒星具有旋转对称性。 不管哪个点旋转到顶部, 它看起来都是一样的。 因为有 5 个点, 这是一个数字, 旋转对称为 5 。Examples
::实例Example 1
::例1Earlier, you were given a problem about Raven and her cat.
::早些时候,你得到一个问题 关于乌鸦和她的猫。Raven notices that her cat's face looks symmetrical. What type(s) of line symmetry does Raven's cat have?
::Raven注意到她的猫的脸看起来对称, Raven的猫有哪几条线对称?First, draw a vertical line down the middle of the cat's face. Does the line divide the cat's face in to halves that look the same?
::首先,在猫的脸上划一条垂直线。这条线是否将猫的脸分割成看起来相同的一半?Yes
::是 是Next, draw a horizontal line down the middle of the cat's face. Does the line divide the cat's face in to halves that look the same?
::接下来,在猫的脸上画一条水平线。这条线能把猫的脸分割到看起来相同的一半吗?No
::否 无Then, state the lines of symmetry.
::然后,说明对称的线条。Vertical
::垂直垂直垂直The answer is that the cat's face has a vertical line of symmetry.
::答案是猫的脸有垂直的对称线Example 2
::例2Identify the lines of symmetry in the object.
::识别对象中的对称线。First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
::首先, 在形状中间绘制一条垂直线。 线条将对象分隔为看起来相同的半径吗 ?Yes
::是 是Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?
::下一步, 在形状中间绘制一条水平线。 线条将对象分隔为看起来相同的半径吗 ?No
::否 无Then, state the lines of symmetry.
::然后,说明对称的线条。Vertical
::垂直垂直垂直The answer is that the object has a vertical line of symmetry.
::答案是,该对象的垂直对称线是垂直的。Example 3
::例3Identify the lines of symmetry in the object.
::识别对象中的对称线。First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
::首先, 在形状中间绘制一条垂直线。 线条将对象分隔为看起来相同的半径吗 ?Yes
::是 是Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?
::下一步, 在形状中间绘制一条水平线。 线条将对象分隔为看起来相同的半径吗 ?Yes
::是 是Then, state the lines of symmetry.
::然后,说明对称的线条。Vertical and horizontal
::垂直和水平The answer is that the object has vertical and horizontal lines of symmetry.
::答案是对象具有垂直和水平对称线。Example 4
::例4Identify the lines of symmetry in the object.
::识别对象中的对称线。First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
::首先, 在形状中间绘制一条垂直线。 线条将对象分隔为看起来相同的半径吗 ?No
::否 无Next, draw a horizontal line down the middle of the shape. Does the line divide the object in halves that look the same?
::下一步, 在形状中间绘制一条水平线。 线条将对象分隔为看起来相同的半径吗 ?Yes
::是 是Then, state the lines of symmetry.
::然后,说明对称的线条。Horizontal
::水平水平水平
The answer is that the object has a horizontal line of symmetry.
::答案是,对象具有对称水平线。Example 5
::例5Identify the lines of symmetry in the object.
::识别对象中的对称线。First, draw a vertical line down the middle of the shape. Does the line divide the object in halves that look the same?
::首先, 在形状中间绘制一条垂直线。 线条将对象分隔为看起来相同的半径吗 ?Yes
::是 是Next, draw lines from the middle of each side to the point opposite of it. Do both of the lines divide the object in halves that look the same?
::下一步, 从每侧中间划线到对面的点。 两条线将对象分隔为看起来相同的半径吗 ?Yes
::是 是Then, state the lines of symmetry.
::然后,说明对称的线条。One line of symmetry from each vertex to the middle of the opposite side for a total of three lines of symmetry.
::从每个顶端到对面的中间一行对称,总共三行对称。The answer is that the shape has three lines of symmetry, one from each vertex to the middle of the opposite side.
::答案是形状有三条对称线, 从每个顶端到对面的中间各一条。Review
::回顾Identify the lines of symmetry in each figure or object. Draw them in if possible.
::识别每个图或对象的对称线。如果可能,请绘制这些线。-
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::[图17]
Identify whether the following objects have rotational symmetry. If yes, write yes. If no, write no.
::标明下列对象是否具有旋转对称性。如果为是,请写是。如果为否,请写否。-
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::[表23]
Find three other objects. Draw them and identify each line of symmetry. Share your findings with a friend.
::查找另外三个对象。 绘制它们并确定每一对称线。 与朋友分享您的发现 。Review (Answers)
::回顾(答复)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 。Resources
::资源
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