9.16同形图对应部分

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  同形图对应部分

  

  [Figure 1]

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  Melvin lives in a house that has a lot of mirrors. He enjoys looking in the mirrors and playing with the mirrors. One day, his mother tells him that the   shaped mirror by the front door is  congruent  to the parallelogram shaped mirror next to the pictures in the hallway. Melvin draws the to shapes as best as he can and labels the parts that he knows for each shape.
  ::Melvin住在一个有很多镜子的房子里。他喜欢看镜子,喜欢玩镜子。有一天,他母亲告诉他,前门的外形镜子与走廊照片旁边的平行图面镜子一样。Melvin尽可能地画出形状,并贴上他所知道的每个形状的形状。

  

  [Figure 2]

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  What is the length of  $\begin{array}{r}\overline{AB}\end{array}$ ?
  ::A B的长度是多少?

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  In this concept, you will learn about  corresponding  parts of congruent figures.
  
  ::在此概念中,您将了解相同数字的相应部分。

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  Corresponding Parts of Congruent Figures
  ::相对应的相近数字部分

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  The word  corresponding  refers to parts that match between two  . You can identify   and  corresponding sides .
  ::对应的字词是指匹配两个部分。您可以辨别和对应的两边。

  

  [Figure 3]

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  First, name the corresponding angles. Corresponding angles are matching  angles  between the two triangles. Corresponding angles will have the same  measure  in congruent triangles.
  ::首先,指定相应的角度。对应角度是两个三角形之间的匹配角度。对应角度在相匹配三角形中将具有相同的度量。

  $$\begin{array}{r}\mathrm{\angle }A\cong \mathrm{\angle }D\\ \mathrm{\angle }B\cong \mathrm{\angle }E\\ \mathrm{\angle }C\cong \mathrm{\angle }F\end{array}$$

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  Here the angles are connected with the symbol for congruent. When you see the equals sign with a squiggly  line  on top, you know that the items on each side of the equation are congruent.
  ::这里的角度与符号相连接, 以求一致。 当您看到等值符号时, 上面有一条粘结的线条, 您知道方程的每侧的项目是相容的 。

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  Next, name the corresponding sides. Corresponding sides are matching sides between two triangles. They will have the same length in congruent triangles.
  ::下一个点出对应的边。 对应的边对齐两个三角形之间的边。 它们具有相同的三角形长度 。

  $$\begin{array}{r}\overline{AB}\cong \overline{DE}\\ \overline{AC}\cong \overline{DF}\\ \overline{BC}\cong \overline{EF}\end{array}$$

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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 Melvin and his house of mirrors.
  ::早些时候,有人给了你一个问题 关于梅尔文和他的镜子房子。

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  He learns that two of the mirrors are congruent, so he draws the shapes as best as he can and fills in what he knows about each shape.
  ::他学会了两面镜子是相似的, 所以他尽可能地画出形状, 并填充他所知道的每一个形状。

  

  [Figure 4]

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  What is the length of  $\begin{array}{r}\overline{AB}\end{array}$ ?
  ::A B的长度是多少?

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  First, rotate the second shape so that it looks the same as the first shape.
  ::首先,旋转第二个形状,让它看起来和第一个形状一样。

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  Next, identify the side on the second  triangle  that corresponds to  $\begin{array}{r}\overline{AB}\end{array}$ .
  ::下一个,确定第二个三角形的侧面 对应的A B'。

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  $\begin{array}{r}\overline{PQ}\end{array}$
  ::P Q 语

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  Then, write the length of the corresponding side.
  ::然后,写下相应边的长度。

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  7 cm
  ::7厘米 7厘米

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  The answer is 7 cm. The length of  $\begin{array}{r}\overline{AB}\end{array}$  is 7 cm.
  ::答案是7厘米,AB的长度是7厘米

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  Example 2
  ::例2

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  These two figures are congruent. Which angle is congruent to angle  $\begin{array}{r}A\end{array}$ ?
  ::这两个数字是相同的。哪个角度与 A 角度一致?

  

  [Figure 5]

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  First, turn the second figure so that it is arranged like the first shape.
  ::首先,翻转第二个数字,这样它就和第一个形状一样排列。

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  Then, identify the angle on the second figure that is in the same position as angle  $\begin{array}{r}A\end{array}$  in the first triangle.
  ::然后,确定第二个图中与第一个三角形中A角位置相同的角度。

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    $\begin{array}{r}P\end{array}$
  ::P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P

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  The answer is angle  $\begin{array}{r}P\end{array}$ .  $\begin{array}{r}\mathrm{\angle }A\cong \mathrm{\angle }Q\end{array}$
  ::答案是角度P.

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  Use the following  diagram  of two congruent triangles to answer the following questions.
  ::使用下图两个相似的三角形来回答下列问题。

  

  [Figure 6]

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  Example 3
  ::例3

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  Angle  $\begin{array}{r}E\end{array}$  is congruent to angle _____
  ::角度 E 与角度 等同 __

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  First, make sure that the triangles are arranged so that they look the same.
  ::首先,确保三角形的排列使其看起来相同。

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  Yes
  ::是 是

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  Then, identify the angle on the second triangle that is in the position that angle  $\begin{array}{r}E\end{array}$  is in the first triangle.
  ::然后,确定第二个三角形的角,即角E位于第一个三角形的角。

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    $\begin{array}{r}H\end{array}$
  ::赫 时

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  The answer is angle  $\begin{array}{r}H\end{array}$ . Angle  $\begin{array}{r}E\end{array}$  is congruent to angle  $\begin{array}{r}H\end{array}$ .
  ::答案是角 H. 角 E 与角 H 一致 。

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  Example 4
  ::例4

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  $\begin{array}{r}\overline{FG}\cong \underset{\_}{}\end{array}$
  ::{\fn方正黑体简体\fs18\b1\bord1\shad1\3cH2F2F2F}F G

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  First, make sure that the triangles are arranged so that they look the same.
  ::首先,确保三角形的排列使其看起来相同。

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  Yes
  ::是 是

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  Then, identify the  line segment  on the second triangle that is in the position that  $\begin{array}{r}\overline{FG}\end{array}$  is in the first triangle.
  ::然后,确定第二个三角形上的线段 位置是FG在第一个三角形上

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    $\begin{array}{r}\overline{IJ}\end{array}$
  ::# 我 # # # # # I # # # I # # # I # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

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  The answer is  $\begin{array}{r}\overline{IJ}\end{array}$ .  $\begin{array}{r}\overline{FG}\cong \overline{IJ}\end{array}$ .
  ::答案是"我","我","我","我","我"

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  Example 5
  ::例5

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  Angle  $\begin{array}{r}J\end{array}$  is congruent to angle _____
  ::角度 J 与角度 等同 __

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  First, make sure that the triangles are arranged so that they look the same.
  ::首先,确保三角形的排列使其看起来相同。

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  Yes
  ::是 是

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  Then, identify the angle on the second triangle that is in the position that angle  $\begin{array}{r}J\end{array}$  is in the first triangle.
  ::然后,确定第二个三角形的角,这个角的位置是 J 在第一个三角形的角。

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    $\begin{array}{r}G\end{array}$
  ::G 级

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  The answer is angle  $\begin{array}{r}G\end{array}$ . Angle  $\begin{array}{r}J\end{array}$  is congruent to angle  $\begin{array}{r}G\end{array}$ .
  
  ::答案是角度 G. agle J 与角度 G 一致 。

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  Review
  ::回顾

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  Use the following triangles to answer the questions.
  ::使用以下三角形回答问题。

  

  [Figure 7]

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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. Side  $\begin{array}{r}DE\end{array}$  is congruent to which other side?
     ::DE侧与另一侧一致?
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  4. Side  $\begin{array}{r}DF\end{array}$  is congruent to which other side?
     ::DF侧与另一侧一致?
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  5. Side  $\begin{array}{r}EF\end{array}$  is congruent to which other side?
     ::EF侧与另一侧一致吗?
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  6. If the side length of  $\begin{array}{r}DE\end{array}$  is 10, what is the side length of  $\begin{array}{r}GH\end{array}$ ?
     ::如果D E的侧长是10,G H的侧长是多少?
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  7. If the side length of  $\begin{array}{r}HI\end{array}$  is 8, which other side is also 8?
     ::如果H I的侧长是8, 那另一边也是8?

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  Use the parallelograms below to answer the following questions.
  ::使用下面的平行图形回答下列问题。

  

  [Figure 8]

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  8. These two figures are congruent. Explain two ways that you can determine whether or not figures are congruent.
     ::这两个数字是一致的。请解释两种方法来判断数字是否一致。
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  9. Angle Q is congruent to which other angle?
     ::角度 Q 是否与其他角度一致 ?
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  10. Angle R is congruent to which other angle?
      ::角度 R 与其他角度一致吗 ?
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  11. Angle S is congruent to which other angle?
      ::角度 S 与哪个其他角度一致 ?
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  12. If PQ is 7 cm, which other sides are 7 cm?
      ::如果PQ是7厘米,另一边是7厘米?
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  13. If QR is 4 cm, which other sides are 4 cm?
      ::如果QR为4厘米,另一边为4厘米?
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  14. If Angle D is 70 degrees, name another 70 degree angle.
      ::如果 Agle D 是 70 度, 请另指定 70 度角度 。
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  15. If Angle A is 110 degrees, name another 110 degree angle.
      ::如果 A 角度 A 是 110 度, 请另指定 110 度角度 。

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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