4.4 一致声明

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  一致发言

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  Congruence Statements
  ::一致发言

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  When stating that two triangles are congruent , the corresponding parts must be written in the same order. For example, if we know that $\begin{align*}\triangle ABC\end{align*}$ and $\begin{align*}\triangle LMN\end{align*}$ are congruent then we know that:
  ::当声明两个三角是相同的时, 相应的部分必须按相同的顺序写。 例如, 如果我们知道 QABC 和 QLMN 是相同的, 那么我们就会知道 :

  

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  Notice that the congruent sides also line up within the congruence statement.
  ::请注意,一致的方面也排在一致的声明中。

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  $\begin{align*}\overline{AB} \cong \overline{LM}, \ \overline{BC} \cong \overline{MN}, \ \overline{AC} \cong \overline{LN}\end{align*}$
  ::阿BLM,不,不,不,阿CLN

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  We can also write this congruence statement five other ways, as long as the congruent angles match up. For example, we can also write $\begin{align*}\triangle ABC \cong \triangle LMN\end{align*}$ as:
  ::我们也可以用其他五种方式写出这个一致的语句,只要一致的角度相匹配。例如,我们也可以将“ABC”和“LMN”写成:

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  $$\begin{align*}&\triangle ACB \cong \triangle LNM && \triangle BCA \cong \triangle MNL && \triangle BAC \cong \triangle MLN\\ &\triangle CBA \cong \triangle NML && \triangle CAB \cong \triangle NLM && \end{align*}$$
  ::* ACBLNMBAMANBACMLNCBANLCABNLM

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  What if you were told that $\begin{align*}\triangle FGH \cong \triangle XYZ\end{align*}$ ? How could you determine which side in $\begin{align*}\triangle XYZ\end{align*}$ is congruent to $\begin{align*}\overline{GH}\end{align*}$ and which angle is congruent to $\begin{align*}\angle{F}\end{align*}$ ?
  ::狦砆禗 或絋)XYZ娩cmGHGHcmF娩琌娩 娩cmF娩琌娩

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  Examples
  ::实例

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  Example 1
  ::例1

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  If $\begin{align*}\triangle ABC \cong \triangle DEF\end{align*}$ , what else do you know?
  ::如果ABCDEF,你还知道什么?

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  From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. $\begin{align*} \angle{A} \cong \angle{D}, \angle{B} \cong \angle{E}, \angle{C} \cong \angle{F}\end{align*}$ , $\begin{align*}\overline{AB} \cong \overline{DE}, \ \overline{BC} \cong \overline{EF}, \ \overline{AC} \cong \overline{DF}\end{align*}$ .
  ::从这份一致声明中,我们知道三对角度和三对方是相同的。 AD, BE, CF, AB DE, BC E, AC DF。

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  Example 2
  ::例2

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  If $\begin{align*}\triangle KBP \cong \triangle MRS\end{align*}$ , what else do you know?
  ::如果KBPZMS,你还知道什么?

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  From this congruence statement, we know three pairs of angles and three pairs of sides are congruent. $\begin{align*} \angle{K} \cong \angle{M}, \angle{B} \cong \angle{R}, \angle{P} \cong \angle{S}\end{align*}$ , $\begin{align*}\overline{KB} \cong \overline{MR}, \ \overline{BP} \cong \overline{RS}, \ \overline{KP} \cong \overline{MS}\end{align*}$ .
  ::从这份一致声明中,我们知道三对角度和三对方是相同的。 @KM,BR,PS,KBM,BPRS,KPMS。

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  Example 3
  ::例3

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  Write a congruence statement for the two triangles below.
  ::为以下两个三角写一个一致语句。

  

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  Line up the in the triangles:
  ::在三角形上行 :

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  $\begin{align*}\angle{R} \cong \angle{F}, \ \angle{S} \cong \angle{E}\end{align*}$ , and $\begin{align*}\angle{T} \cong \angle{D}\end{align*}$ .
  ::,

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  Therefore, one possible congruence statement is $\begin{align*}\triangle RST \cong \angle{FED}\end{align*}$
  ::因此,一个可能一致的说法是“RST”和“FED”。

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  Example 4
  ::例4

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  If $\begin{align*}\triangle CAT \cong \triangle DOG\end{align*}$ , what else do you know?
  ::如果"CATODOG",你还知道什么?

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  From this congruence statement, we know three pairs of angles and three pairs of sides are congruent.
  ::从这份一致声明中,我们知道三对角度和三对方是一致的。

  

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  Example 5
  ::例5

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  If $\begin{align*}\triangle BUG \cong \triangle ANT\end{align*}$ , what angle is congruent to $\begin{align*}\angle{N}\end{align*}$ ?
  ::如果ZZBUGANT,什么角度与NQN一致?

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  Since the order of the letters in the congruence statement tells us which angles are congruent, $\begin{align*}\angle{N} \cong \angle{U}\end{align*}$ because they are each the second of the three letters.
  ::由于一致声明中字母的顺序告诉我们哪个角度是相同的,所以NU,因为它们是三个字母中的第二个。

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  Review
  ::回顾

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  For questions 1-4, determine if the triangles are congruent using the definition of congruent triangles. If they are, write the congruence statement.
  ::对于问题1-4, 使用对齐三角的定义确定三角形是否一致。 如果一致, 请写一致的语句 。

  1. 
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  5. Suppose the two triangles below are congruent. Write a congruence statement for these triangles.
     ::假设下面的两个三角形是相同的。 为这些三角形写一个一致的语句 。
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  6. Explain how we know that if the two triangles are congruent, then $\begin{align*}\angle{B} \cong \angle{Z}\end{align*}$ .
     ::解释我们如何知道,如果这两个三角形是相同的,那么,"B"。
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  7. If $\begin{align*}\triangle TBS \cong \triangle FAM\end{align*}$ , what else do you know?
     ::如果TBSFAM,你还知道什么?
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  8. If $\begin{align*}\triangle PAM \cong \triangle STE\end{align*}$ , what else do you know?
     ::如果"PAMSTE,你还知道什么?
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  9. If $\begin{align*}\triangle INT \cong \triangle WEB\end{align*}$ , what else do you know?
     ::如果NTZWEB,你还知道什么?
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  10. If $\begin{align*}\triangle ADG \cong \triangle BCE\end{align*}$ , what angle is congruent to $\begin{align*} \angle{G}\end{align*}$ ?
      ::如果“ADGBCE”,什么角度与“G”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