6.6 草类

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  细胞类

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  Trapezoids
  ::细胞类

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  A trapezoid is a quadrilateral with exactly one pair of parallel sides.
  ::甲状腺类是一种四边形, 有着一对齐的平行面。

  

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  An isosceles trapezoid is a trapezoid where the non-parallel sides are congruent .
  ::等离子体类是非平行面相似的类类。

  

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  The base angles of an isosceles trapezoid are congruent. If $\begin{align*}ABCD\end{align*}$ is an isosceles trapezoid, then $\begin{align*}\angle A \cong \angle B\end{align*}$ and $\begin{align*}\angle C \cong \angle D\end{align*}$ .
  ::asosceles capezoid 的底角是相似的。 如果 ABCD 是 asosceles capezoid, 则 {AB 和 {CD } 。

  

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  The converse is also true. If a trapezoid has congruent base angles, then it is an isosceles trapezoid. The diagonals of an isosceles trapezoid are also congruent. The midsegment (of a trapezoid) is a line segment that connects the midpoints of the non-parallel sides:
  ::反之, 反之亦然 。 如果一个陷阱类具有相容的底角, 那么它就是一个等骨类底角 。 等骨类底座的对角也是相似的 。 中间部分( 类) 是连接非平行边中点的线条段 :

  

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  There is only one midsegment in a trapezoid. It will be parallel to the bases because it is located halfway between them.
  ::捕鲸类中只有一个中间部分。 它会与基地平行, 因为它位于它们中间的半个位置 。

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  Midsegment Theorem : The length of the midsegment of a trapezoid is the average of the lengths of the bases.
  ::密段定理 : 网格类的中间部分长度是基底长度的平均值 。

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  If $\begin{align*}\overline{EF}\end{align*}$ is the midsegment, then $\begin{align*}EF = \frac{AB + CD}{2}\end{align*}$ .
  ::如果EF是中间部分,那么EF=AB+CD2。

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  What if you were told that the polygon  $\begin{align*}ABCD\end{align*}$ is an isosceles trapezoid and that one of its base angles measures $\begin{align*}38^\circ\end{align*}$ ? What can you conclude about its other base angle ? 
  ::如果有人告诉您多边形ABCDIS 等离子体细胞类和其基角之一测量38+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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  Examples
  ::实例

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  For Examples 1 and 2, use the following information:
  ::关于例1和例2,请使用以下信息:

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  $\begin{align*}TRAP\end{align*}$  is an isosceles trapezoid.
  ::TRAP是一个等骨细胞类。

  

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  Example 1
  ::例1

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  Find  $\begin{align*}m \angle TPA\end{align*}$ .
  ::找到MTPA。

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  $\begin{align*}\angle TPZ \cong \angle RAZ\end{align*}$ so $\begin{align*}m\angle TPA=20^\circ + 35^\circ = 55^\circ\end{align*}$ .
  ::~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

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  Example 2
  ::例2

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  Find  $\begin{align*}m \angle ZRA\end{align*}$ .
  ::去找玛拉

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  Since $\begin{align*}m\angle PZA = 110^\circ\end{align*}$ , $\begin{align*}m\angle RZA=70^\circ\end{align*}$ because they form a linear pair . By the Triangle Sum Theorem, $\begin{align*}m\angle ZRA=90^\circ\end{align*}$ .
  ::自 mPZA=110, mRZA=70 因为它们形成直线对。 依三角形sumTheorem, mRA=90。

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  Example 3
  ::例3

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  Look at trapezoid $\begin{align*}TRAP\end{align*}$ below. What is $\begin{align*}m \angle A\end{align*}$ ?
  ::看看下面的陷阱图 是什么?

  

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  $\begin{align*}TRAP\end{align*}$ is an isosceles trapezoid. $\begin{align*}m \angle R = 115^\circ\end{align*}$ also.
  ::TRAP 是一个等离子细胞类。 mR=115。

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  To find $\begin{align*}m \angle A\end{align*}$ , set up an equation.
  ::为了找到maA, 设置一个方程。

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  $$\begin{align*}115^\circ + 115^\circ + m \angle A + m \angle P & = 360^\circ\\ 230^\circ + 2m \angle A & = 360^\circ \qquad \rightarrow m \angle A = m \angle P\\ 2m \angle A & = 130^\circ\\ m \angle A & = 65^\circ\end{align*}$$
  ::$115mA+mP=3602302A=360mA=mP2A=130mA=65

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  Notice that $\begin{align*}m \angle R + m \angle A = 115^\circ + 65^\circ = 180^\circ\end{align*}$ . These angles will always be supplementary because of the Consecutive Interior Angles Theorem.
  ::注意 mR+mA=11565 180。 这些角度将永远是补充的, 因为有连续的内脏角度定理 。

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  Example 4
  ::例4

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  Is $\begin{align*}ZOID\end{align*}$ an isosceles trapezoid? How do you know?
  ::ZOID是不是一个异骨骼类动物?你怎么知道的?

  

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  $\begin{align*}40^\circ \neq 35^\circ\end{align*}$ , $\begin{align*}ZOID\end{align*}$ is not an isosceles trapezoid.
  ::4035, ZOID 不是一个等离子体。

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  Example 5
  ::例5

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  Find $\begin{align*}x\end{align*}$ . All figures are trapezoids with the midsegment marked as indicated.
  ::查找 x. 所有数字都是插件,中间部分标记如上所示。

  1. 

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    $\begin{align*}x\end{align*}$ is the average of 12 and 26. $\begin{align*}\frac{12 + 26}{2} = \frac{38}{2} = 19\end{align*}$
  ::x是12和26.12+262=382=19的平均值

  2. 

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   24 is the average of $\begin{align*}x\end{align*}$ and 35.
  ::24是x和35的平均数。

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  $$\begin{align*}\frac{x + 35}{2} & = 24\\ x + 35 & = 48\\ x & = 13\end{align*}$$
  ::x+352=24x+35=48x=13

  3. 

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   20 is the average of $\begin{align*}5x - 15\end{align*}$ and $\begin{align*}2x - 8\end{align*}$ .
  ::20是5x-15和2x-8的平均值。

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  $$\begin{align*}\frac{5x - 15 + 2x - 8}{2} & = 20\\ 7x - 23 & = 40\\ 7x & = 63\\ x & = 9\end{align*}$$
  ::5-15+2x-82=207x-23=407x=63x=9

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  Review
  ::回顾

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  1. Can the parallel sides of a trapezoid be congruent? Why or why not?
  ::1. 围网类的平行面能否一致?为什么或为什么不能?

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  For questions 2-8, find the length of the midsegment or missing side.
  ::对于问题2-8,请找到中间部分的长度或缺失的侧面。

  2. 
  3. 
  4. 
  5. 
  6. 
  7. 

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  Find the value of the missing variable(s).
  ::查找缺失变量的值。

  8. 

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  Find the lengths of the diagonals of the trapezoids below to determine if it is isosceles.
  ::查找下面的捕捉类星体的对角长度,以确定它是否为等分形。

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  9. $\begin{align*}A(-3, 2), B(1, 3), C(3, -1), D(-4, -2)\end{align*}$
     ::A(3,3,2),B(1,3,3),C(3,-1),D(-4,4)-2
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  10. $\begin{align*}A(-3, 3), B(2, -2), C(-6, -6), D(-7, 1)\end{align*}$
      ::A(-3,3),B(2,-2),C(-6,-6),D(-7,1)

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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 。