8.17 对称线
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Cassie works at an apple orchard. She mostly works in the store and sells the products, but she loves going to the orchard and picking fresh apples off the trees. She has noticed that most, but not all of the apples are symmetrical. She cuts one apple in half and notices that the symmetry continues on the inside. Does the apple have line symmetry , rotational symmetry , both or neither?
::Cassie在苹果园工作。她大部分在商店工作,出售产品,但她喜欢去果园,从树上摘取新鲜苹果。她注意到大部分苹果都是对称的,但并非所有苹果都是对称的。她把苹果切成两半,并且注意到内部对称性还在继续。苹果有线对称性、旋转对称性,还是两者都没有?In this concept, you will learn about lines of symmetry.
::在这个概念中,你会了解对称的线条。Lines of Symmetry
::对称线线A line that acts as a mirror is called a line of symmetry . Symmetry means that when you divide a figure in half, the halves are congruent . In other words, a figure is symmetric if its outlines mirror each other.
::作为镜像的线条被称为对称线。对称法意味着当将一个数字一分为二时,两半是相同的。换句话说,如果一个数字的轮廓对齐,那么一个数字就是对称的。Look at the figure below. Imagine you can fold it in half. When you fold it, do the outlines of each half match? They do, so this figure has symmetry.
::看看下方的图。 想象一下你可以把它折成两半。 当你折成两半时, 做每半匹配的轮廓。 他们这样做, 所以这个数字是对称的 。When you “unfold” the figure, you have two congruent halves. The “fold” line is the line of symmetry. It divides the figure into halves that are mirror images of each other. Every part on one half “mirrors” or corresponds to a part on the other half.
::当您“ 翻翻” 数字时, 您将有两个相近的半径。 “ 倍平” 线是对称线。 它将数字分成两半, 它们是彼此的镜像。 每半“ mirrors” 上的每一部分或对应另一半的某一部分 。Let's look at an example. Can you fold the figure perfectly in half?
::让我们举个例子。你能把数字完全折成两半吗?You can try to fold this figure a bunch of different ways, but it does not have a line of symmetry.
::你可以试着用不同的方式折叠这个数字, 但它没有对称性。Rotational symmetry is a different kind of symmetry. It means that when you rotate a figure, the figure appears to stay the same. The outlines do not change even as the figure turns. Look at the figure below.
::旋转对称是一种不同的对称。 这意味着, 当您旋转一个图时, 图似乎保持不变。 轮对称即使在图转动时, 轮对称也不会改变。 请看下图 。You can tell the figure has been rotated because the dot moves clockwise. However, the outlines of the figure have not changed. This figure has rotational symmetry because every time you turn it, one of the arms of the star always faces up.
::您可以通过圆点顺时针移动来判断数字的旋转情况。 但是, 图的轮廓没有改变。 此图具有旋转对称性, 因为每次转动时, 恒星的臂部总是向上显示 。Examples
::实例Example 1
::例1Earlier, you were given a problem about Cassie and the apples.
::早些时候,你得到一个问题 凯西和苹果。Look at the apple that she cut in half. Does the apple have line symmetry, rotational symmetry, both or neither?
::看看她切成两半的苹果。苹果有线对称,旋转对称,两者兼有吗?First, determine if the shape can be folded in half over a line.
::首先,确定形状能否在一条线上半折叠。Yes.
::对Next, determine if the shape will look the same when it is rotated.
::下一步, 确定在旋转时形状是否看起来相同 。No.
::没有 No.Then, state the type of symmetry that the figure has.
::然后,说明数字的对称类型。Line symmetry.
::线性对称 。The answer is that the figure has line symmetry.
::答案是这个数字有线对称。Example 2
::例2Does the figure below have rotational symmetry?
::下图是否具有旋转对称性?First, note the appearance of the figure as it turns.
::首先,注意数字在转动时的外观。The figure has a different appearance for each turn.
::数字每个转弯都有不同的外观。Next, remember the definition of rotational symmetry.
::接下来,记住旋转对称的定义。The figure appears to stay the same.
::这一数字似乎保持不变。Then, state whether the figure has rotational symmetry.
::然后,请说明数字是否具有旋转对称性。No.
::没有 No.
The answer is that the figure does not have rotational symmetry.
::答案是,该数字没有旋转对称。Example 3
::例3Does the following figure have line symmetry, rotational symmetry, both, or neither?
::下图是否具有线对称、旋转对称,两者兼有,还是两者都没有?First, determine if the shape can be folded in half over a line.
::首先,确定形状能否在一条线上半折叠。Yes.
::对Next, determine if the shape will look the same when it is rotated.
::下一步, 确定在旋转时形状是否看起来相同 。Yes.
::对Then, state the type of symmetry that the figure has.
::然后,说明数字的对称类型。Line symmetry and rotational symmetry.
::线对称和旋转对称The answer is that the figure has both line symmetry and rotational symmetry.
::答案是,该数字既有线对称法,也有旋转对称法。Example 4
::例4First, determine if the shape can be folded in half over a line.
::首先,确定形状能否在一条线上半折叠。Yes.
::对Next, determine if the shape will look the same when it is rotated.
::下一步, 确定在旋转时形状是否看起来相同 。No.
::没有 No.Then, state the type of symmetry that the figure has.
::然后,说明数字的对称类型。Line symmetry.
::线性对称 。The answer is that the figure has line symmetry.
::答案是这个数字有线对称。Example 5
::例5First, determine if the shape can be folded in half over a line.
::首先,确定形状能否在一条线上半折叠。Yes.
::对Next, determine if the shape will look the same when it is rotated.
::下一步, 确定在旋转时形状是否看起来相同 。No.
::没有 No.Then, state the type of symmetry that the figure has.
::然后,说明数字的对称类型。Line symmetry.
::线性对称 。The answer is that the figure has line symmetry.
::答案是这个数字有线对称。Review
::回顾Answer each of the following questions true or false.
::回答以下每一个问题是否真实或虚假。-
A reflection has rotational symmetry.
::反射具有旋转对称性。 -
A square has line symmetry and rotational symmetry.
::方形有线对称和旋转对称。 -
If a figure is a transformation than it always rotates clockwise.
::如果数字是一个变化, 而不是它总是顺时针旋转 。 -
A slide is also called a translation.
::幻灯片也称为翻译。 -
A flip has a line of symmetry because it is a reflection.
::翻转具有对称性,因为它是反射。 -
A rotation or turn always moves clockwise and never counterclockwise.
::旋转或转弯总是顺时针,从不逆时针。 -
A star has rotational and line symmetry.
::恒星具有旋转和直线对称性。 -
An regular octagon has rotational and line symmetry.
::普通八边形具有旋转和线对称。
Tell whether the figures below have line symmetry, rotational symmetry, both, or neither.
::说明下图是否具有线对称、旋转对称,或两者兼有。Draw the second half of each figure, and then rotate the figure.
::绘制每个图的后半部分,然后旋转图。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 -
A reflection has rotational symmetry.
