6.7 四方的分类

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  分类四边债

  

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  A yurt is the traditional dwelling of the nomads of Mongolia. This tent-like circular structure is a domed home made from a wooden frame and has lattice walls made of flexible wood. These lattice walls are made in sections of crisscrossed wooden poles attached together with leather ties.
  ::这种帐篷般的圆形结构是用木制木板制成的圆形房屋,有用软木制成的挂板墙。 这些挂板墙是用与皮革领带连在一起的圆形木柱形十字路段制成的。

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  If you were to draw a picture to represent one section of the lattice wall, what type of quadrilateral would you have to draw to represent a section of crisscrossed poles?
  ::如果您要绘制一张图片来代表 长边墙的一个部分, 您需要绘制哪一种四边形来代表 十字路口的一块冰柱?

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  In this concept, you will learn to classify quadrilaterals.
  ::在这个概念中,你会学会四边形的分类。

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  Classifying Quadrilaterals
  ::分类四边债

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  A quadrilateral is a two-dimensional (a flat shape) closed shape that has four straight sides. The word quadrilateral defines itself since ‘quad’ means four and ‘lateral’ means sides. Included in this broad category of four-sided figures are special types of quadrilaterals.
  ::一个四边形是一个双维(一个平面)封闭的形状,有四个直面。四边形一词定义了自己,因为“四边形”是指四面形,“四边形”是指四面形。 包括四面形图在内的四面形图的大类中包括特殊类型的四边形。

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  The first special quadrilateral is a . A parallelogram is a quadrilateral with opposite sides parallel and congruent . The following diagram is a parallelogram.
  ::第一个特殊四边形是 。 平行图是两面平行和一致的四边形。 下图是一个平行图。

  

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  Notice that sides $\begin{array}{r}\begin{array}{rcl}\overline{AB}& \cong & \overline{CD}\\ \overline{AB}& ||& \overline{CD}\end{array}\end{array}$  and sides  $\begin{array}{r}\begin{array}{rcl}\overline{AC}& \cong & \overline{BD}\\ \overline{AC}& ||& \overline{BD}\end{array}\end{array}$ . Remember parallel means the parallel sides are always the same distance apart and they will never intersect. The congruent sides are equal in length.
  ::请注意 AB 和 AC 和 AC BD 的两边。 记住, 平行的两边永远是相同的距离, 永远不会交叉。 一致的两边是相同的长度 。

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  There are three types of parallelograms.
  ::平行图有三种类型。

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  One type of parallelogram is called a rectangle . A rectangle is a parallelogram where every angle is a right angle . Also the opposite sides of a rectangle are congruent and parallel. The following diagram is a rectangle.
  ::一种类型的平行图被称作矩形。矩形是一个平行图,其中每个角度都是右角。矩形的对面也是相近和平行的。下图是一个矩形。

  

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  Notice that sides $\begin{array}{r}\begin{array}{rcl}\overline{AB}& \cong & \overline{CD}\\ \overline{AB}& ||& \overline{CD}\end{array}\end{array}$  and sides  $\begin{array}{r}\begin{array}{rcl}\overline{AC}& \cong & \overline{BD}\\ \overline{AC}& ||& \overline{BD}\end{array}\end{array}$ . In addition to the relationships between the opposite sides of the rectangle, all of the angles of the rectangle are right angles.
  ::除了矩形对面的关系外,矩形的所有角度都是正确的角度。

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  A second type of parallelogram is a square . A square is a parallelogram where every angle is a right angle. Opposite sides of the square are parallel and all sides are the same length.
  ::第二种平行图是方形。 方形是平行图, 每个角度都是右角。 方形的对面是平行的, 方形的对面都是相同的长度 。

  

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  Notice that sides $\begin{array}{r}\begin{array}{rcl}\overline{AB}& ||& \overline{CD}\\ \overline{AC}& ||& \overline{BD}\end{array}\end{array}$  and sides $\begin{array}{r}\overline{AC}\cong \overline{BD}\cong \overline{AB}\cong \overline{CD}\end{array}$ . In addition to the relationships between the opposite sides and all sides of the rectangle, all of the angles of the rectangle are right angles.
  ::请注意 AB 和 AC BD 和 AC BD 和 AC BD 和 AB 和 CD 。 除了对立面和矩形两侧之间的关系外, 矩形的所有角度都是正确的角度 。

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  A third type of parallelogram is a rhombus . A rhombus is a parallelogram with every side equal in length. Opposite sides of the rhombus are parallel but the angles are not right angles. The following diagram is a rhombus.
  ::第三种平行图是圆柱形。 圆柱形是一个平行图, 每边长度相等。 圆柱形的对面面是平行的, 但角度不是正确的角度。 下图是圆柱形 。

  

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  Notice that sides $\begin{array}{r}\begin{array}{rcl}\overline{AB}& ||& \overline{CD}\\ \overline{AC}& ||& \overline{BD}\end{array}\end{array}$  and sides $\begin{array}{r}\overline{AC}\cong \overline{BD}\cong \overline{AB}\cong \overline{CD}\end{array}$ .
  ::注意AB和AC和AB和AB的两边

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  Another type of quadrilateral that is not a parallelogram is a trapezoid . A trapezoid is a quadrilateral that has one pair of opposite sides parallel. The non-parallel sides are called the legs of the trapezoid. The angles on the same side of a leg are adjacent angles such that $\begin{array}{r}\mathrm{\angle }A\end{array}$  and $\begin{array}{r}\mathrm{\angle }C\end{array}$  are supplementary. This means $\begin{array}{r}\mathrm{\angle }A+\mathrm{\angle }C={180}^{\circ }\end{array}$ . The following diagram is a trapezoid.
  ::另一种不是平行方形的四边形是形。 形是四边形, 有一对对对面平行。 非平行方面被称为形的腿。 一条腿同一侧的角是相邻角度, 以至于A和C是补充的。 这意味着AC=180。 下图是形。 下图是形 。

  

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  Notice that side $\begin{array}{r}\overline{AB}||\overline{CD}\end{array}$ .
  ::注意AB的侧面

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  What type of quadrilateral has opposite sides congruent and parallel? Every angle is not a right angle.
  ::哪种四边形的对立面是相似和平行的?每个角度都不是正确的角度。

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  A parallelogram has opposite sides congruent and parallel and every angle is not a right angle.
  ::平行图面的两侧相近和平行,每个角度都不是正确的角度。

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  Another type of quadrilateral is called a . A kite is a flat shape such that it has two pairs of congruent adjacent sides. The angles where the two pairs meet are also congruent in measure . The following diagram is a kite.
  ::另一种类型的四边形被称为 a。风筝是一个平坦的形状,它有两对相近的相近边。两对相交的角也相匹配。下图是风筝。

  

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  Examples
  ::实例

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  Example 1
  ::例1

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  Remember the yurt? You need to figure out the type of quadrilateral used to form the lattice walls.
  ::记得卷发吗?你需要弄清楚 用来形成圆顶墙的四边形

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  The sides of each figure created by the lattice are all equal in length. This may make you think that this is definitely a square. However, if you look at the angles, the angles are not right angles. Therefore, it can’t be a square. In fact, it is actually a rhombus. Remember a rhombus has four sides of equal length, opposite sides are equal and parallel, but every angle is not a right angle.
  ::由 挂式 所 创造 的 每 个 数字 的 侧面 长度 都 相等 。 这可能 使 你 认为 这 绝对 是 方形 。 但是, 如果 从 角度 来看 , 角度 不 正确 。 因此, 角度 并不是 方形 。 事实上, 它 实际上是 rhombus 。 记住 rhombus 的 四 面 长度 相同 , 反 面 是 平等和 平行 的 , 但 每个 角度 都不是 正确 的 角度 。

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  Example 2
  ::例2

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  What is the name of the four-sided figure that has all sides equal in length, opposite sides parallel and four right angles?
  ::四面数字的长度相等、对面平行和四个右角度的四面数字叫什么?

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  The name of the figure is a square.
  ::数字的名称是一个方形。

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  Example 3
  ::例3

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  How are a parallelogram and a rectangle different?
  ::平行图和矩形如何不同?

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  Remember there are several types of parallelograms. A regular parallelogram has no right angles but every angle of a rectangle is a right angle.
  ::记住有几种平行图。 普通的平行图没有正确的角度, 但矩形的每一个角度都是正确的角度 。

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  Example 4
  ::例4

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  What is the name of the quadrilateral that has one pair of opposite sides parallel?
  ::有对对对平行的四边形的名称是什么?

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  A trapezoid has one pair of opposite sides parallel.
  ::甲状腺类动物有对对对立的两面平行。

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  Example 5
  ::例5

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  What name is given to the quadrilateral that has two pairs of equal adjacent sides?
  ::有两对相等相邻边的四边形的名称是什么?

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  This quadrilateral is called a kite.
  ::这个四边形叫做风筝

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  Review
  ::回顾

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  Identify each quadrilateral based on the description provided.
  ::根据所提供的说明确定每个四边形。

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  1. A figure with four equal sides and four right angles.
  ::1. 数字四面相等,右角四个。

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  2. A figure with opposite sides congruent and parallel.
  ::2. 具有对立面一致和平行的数字。

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  3. A figure with opposite sides congruent and parallel and four right angles.
  ::3. 数字的对面面相同、平行和四个右角度。

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  4. A figure with four sides.
  ::4. 四面数字。

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  5. A figure with four equal sides which may or may not have four right angles.
  ::5. 具有四个平等面的数字,其中可能有或没有四个正确角度。

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  Use what you have learned about quadrilaterals to answer each of the following questions true or false.
  ::使用你学到的关于四边形的知识 回答以下每一个问题 真实的或虚假的

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  6. A quadrilateral can be any four sided figure.
  ::6. 四边形可以是任何四个侧面数字。

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  7. A rectangle is also a parallelogram, but a parallelogram is not necessarily a rectangle.
  ::7. 矩形也是一种平行图,但平行图不一定是矩形。

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  8. A square is never a parallelogram.
  ::8. 方形从来不是平行图。

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  9. A rhombus can be a square.
  ::9. 暴风车可以是广场。

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  10. A square is always a rhombus.
  ::10. 广场始终是暴风雨。

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  11. A rhombus is a parallelogram.
  ::11. 暴风雨是平行图。

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  12. A quadrilateral is a type of parallelogram.
  ::12. 四边形是一种平行图。

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  13. A trapezoid has opposite sides parallel and congruent.
  ::13. 围网类动物的两面平行并一致。

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  14. What does the sum of the angles of a quadrilateral add up to be?
  ::14. 四边形角度之和加起来是什么?

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  15. What is the measure of any given angle in a rectangle?
  ::15. 矩形中任何特定角度的量度是多少?

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  16. What is the measure of any given angle in a square?
  ::16. 方形中任何特定角度的量度是多少?

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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 。