相似图对应部分

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Maria has an art project due for school. She decides to make a small replica of her bedroom. She begins by measuring the  angles  of her bedroom, then she draws  similar  figures. The larger figure represents her bedroom and the smaller figure represents her replica.
::Maria有一个艺术项目要上学。 她决定对卧室做一个小的复制品。 她首先测量卧室的角度,然后绘制类似的数字。 更大的数字代表她的卧室,小的数字代表她的复制品。

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Her bedroom door is located in the middle of  $\begin{array}{r}\overline{IJ}\end{array}$ . For her replica, the door must be placed in the middle of the  corresponding  side. What side of the replica corresponds to  $\begin{array}{r}\overline{IJ}\end{array}$ ?
::她的卧室门位于我J''的中间。对于她的复制品,门必须放在相应的侧面中间。

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In this concept, you will learn about  corresponding sides  of similar figures.

::在这个概念中,你将了解类似数字的相应方面。

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Corresponding Parts of Similar Figures
::类似数字的相应部分

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Triangle   $\begin{array}{r}ABC\end{array}$  is  similar  to triangle  $\begin{array}{r}DEF\end{array}$ . This means that while they are the same shape, they aren’t the same size. In fact, there is a relationship between the corresponding parts of the triangle.
::三角形A B C 与三角形D E F 类似。 这意味着三角形虽然形状相同,但大小不同。 事实上,三角形的相应部分之间存在某种关系。

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The side lengths are corresponding even though they aren’t  congruent . Use the symbol for similar ("~") to show the relationship between the corresponding sides of the two triangles.
::侧边长度是对应的, 即使它们不相同 。 使用类似符号 (“~ ”) 的符号来显示两个三角形对应的两边之间的关系 。

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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 Maria and her bedroom.
::之前,你得到一个问题 关于玛丽亚和她的卧室。

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She is making a replica of her bedroom for her art class. She draws two similar figures to make sure that she is placing everything in the right position.
::她正在复制她的卧室作为艺术课的复制品。她画了两个相似的数字,以确保她将一切置于正确位置。

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She needs to place her bedroom door in the middle of the side that corresponds to  $\begin{array}{r}\overline{IJ}\end{array}$ . What side corresponds to  $\begin{array}{r}\overline{IJ}\end{array}$ ?
::她需要把她的卧室门放在对应于我J的中间。

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First, rotate the second figure so that it looks like the first figure.
::首先,旋转第二个数字,使其看起来像第一个数字。

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Then, locate the side on the second figure that is in the position that  $\begin{array}{r}\overline{IJ}\end{array}$  is in the first figure.
::然后,找到第二个数字的侧面 处于我J'是第一个数字的位置。

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  $\begin{array}{r}\overline{YZ}\end{array}$
::Y Z , Y Z , Y Z , Y Z , Y Z , Y Z , Y Z

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The answer is that  $\begin{array}{r}\overline{YZ}\end{array}$  corresponds to  $\begin{array}{r}\overline{IJ}\end{array}$ . Maria needs to place her bedroom door in the middle of  $\begin{array}{r}\overline{YZ}\end{array}$  on the replica.
::答案是YZ代表IJ Maria需要把她的卧室门放在YZ中间的复制品上

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Example 2
::例2

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The figures below are similar. What side corresponds  $\begin{array}{r}\overline{NO}\end{array}$ ? 
::以下数字相似。 哪一边对应NO ?

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First, position the second figure so that it looks like the first figure.
::首先,将第二个数字定位到第二个数字,使其看起来像第一个数字。

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Then, identify the side in the second figure that is in the same position as  $\begin{array}{r}\overline{NO}\end{array}$  is in the first figure. 
::然后,在第二个数字中找出与NO位置相同的第二数字的侧面,在第一个数字中找到。

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  $\begin{array}{r}\overline{QR}\end{array}$
::Q R

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The answer is that  $\begin{array}{r}\overline{QR}\end{array}$  corresponds to  $\begin{array}{r}\overline{NO}\end{array}$ .
::答案是QR等于NO。

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Example 3
::例3

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  $\begin{array}{r}\overline{AB}\sim \end{array}$  _____
::一个B ' ' ?

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First, look to see which side in the second triangle corresponds to the given segment.
::首先,看看第二个三角形的哪一边与给定的段相对应。

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  $\begin{array}{r}\overline{EF}\end{array}$
::爱弗费

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Then, complete the problem.
::那就把问题解决了

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  $\begin{array}{r}\overline{AB}\sim \overline{EF}\end{array}$
::一个B''E'F'

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The answer is that  $\begin{array}{r}\overline{AB}\sim \overline{EF}\end{array}$ .
::答案是"B"是"E"

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Example 4
::例4

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What makes the two squares similar if they both have four right angles?
::如果两个方形都有四个右角度, 是什么使这两个方形相似?

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First, check to see if the side lengths are the same.
::首先,检查一下侧边长度是否相同。

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No
::否 无

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Next, check to see if the shape is the same.
::接下来,检查一下形状是否相同。

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Yes
::是 是

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Then, state why the two squares are similar.
::那么,请说明为什么这两个方形相似。

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Same shape, different sizes
::相同形状, 不同大小

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The answer is that the two squares are similar because they have the same shape, but different sizes.
::答案是,这两个方形相似,因为它们的形状相同,但大小不同。

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Example 5
::例5

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In the triangle pair, are the two triangles similar or congruent?
::在三角对中,两个三角是相似的还是相似的?

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First, check to see if the two triangles are the same size.
::首先,检查两个三角形的大小是否相同。

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No
::否 无

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Next, check to see if the two triangles are the same shape.
::下一步,检查两个三角形的形状是否相同。

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Yes
::是 是

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Then, determine if the two triangles are similar or congruent.
::然后,确定这两个三角形是相似的还是相似的。

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Similar
::类似

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The two triangles are similar.
::这两个三角形相似。

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Review
::回顾

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Use the following figures to answer each question.
::使用下列数字回答每个问题。

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1. Are these two triangles similar or congruent?
   ::这两个三角形相似还是相似?
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2. How do you know?
   ::或笵
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3. Which side is congruent to  $\begin{array}{r}\overline{AB}\end{array}$ ?
   ::哪个方面与A B一致?
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4. Which side is congruent to  $\begin{array}{r}\overline{AC}\end{array}$ ?
   ::哪个方面与C一致?
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5. Which side is congruent to  $\begin{array}{r}\overline{RS}\end{array}$ ?
   ::哪个方面与R S一致?
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6. Which angle is congruent to angle A?
   ::哪个角度与 A 角度一致?
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7. Which angle is congruent to angle B?
   ::哪个角度与角度 B 一致 ?
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8. Which angle is congruent to angle C?
   ::哪个角度与 C 角度一致?

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9. Are the two figures similar or congruent?
   ::这两个数字相似还是一致?
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10. Why?
    ::为什么?
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11. Which side is congruent to  $\begin{array}{r}\overline{NO}\end{array}$ ?
    ::哪个方面与NO一致?
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12. Which side is congruent to  $\begin{array}{r}\overline{MN}\end{array}$ ?
    ::哪个方面与MN一致?
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13. Which side is congruent to  $\begin{array}{r}\overline{ST}\end{array}$ ?
    ::哪个方面与S T一致?
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14. Which side is congruent to  $\begin{array}{r}\overline{QT}\end{array}$ ?
    ::哪个方面与Q T一致?
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15. Which side is congruent to  $\begin{array}{r}\overline{OP}\end{array}$ ?
    ::哪个方面与O P 一致?

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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