5.2 三角建设-interactive

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  三角形建设

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  In This Lesson
  ::在本课程中

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  You will begin to learn about how to make triangles and why some side lengths work and some do not. When creating or making geometric figures, it is called constructing .  
  ::您将开始学习如何建立三角形, 为什么有些侧长工作而有些不工作。 当创建或制作几何数字时, 它被称为构建 。

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  A triangle is a 3-sided enclosed shape with three angles . The vertices of the angles are also  the  vertices of the triangle and the three sides are line segments. 
  ::三角形是三面封闭的形状,有三个角度。角的顶部也是三角形的顶部,三面是线条。

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  If two figures have the same measures (angles, side lengths, etc), then those two figures are congruent . Congruent is a way of saying that two geometric figures have the same shape and the same size.  
  ::如果两个数字具有相同的度量(矩形、侧长等),那么这两个数字是相同的。 Congruent 就是说两个几何数字的形状相同,大小相同。

   

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  Three Sides
  ::三面

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  Use the interactive to construct triangles by dragging the three points. Then answer the questions that follow.
  ::使用互动来通过拖曳三点来构造三角形。 然后回答下面的问题 。

   

   

   

   

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  Discussion Question
  ::讨论问题

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  Can any three lengths create a triangle? Create a conjecture about the side lengths of a triangle.
  ::任何三个长度能创建三角形吗? 创建三角形侧长度的猜想 。

   

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  Any Three?
  ::有3个吗?

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  As you determined in the previous interactive, the lengths 3, 4, and 5 created a triangle. However, not every three lengths can create a triangle. Why do some lengths work while others do not?
  ::正如您在上次互动中确定的那样, 长度 3、4 和 5 创建了一个三角形。 但是, 不是每三个长度就能创建三角形。 为什么有些长度工作而另一些长度不工作呢 ?

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  Use this interactive to see if you can come up with a rule regarding the lengths of the sides of triangles. Try to create triangles by moving the red endpoints.
  ::使用此互动来查看您能否就三角形边的长度找到一条规则。 尝试移动红色端点来创建三角形 。

   

   

   

   

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  I n a triangle, the length of a side  must be between  the sum and difference of the other two side lengths. Note that  i t cannot be equal to the sum or difference because that would form a straight line.
  ::在三角形中,侧面的长度必须是其他两侧长度的和和差。请注意,它不能等于和或差,因为这会形成一条直线。

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  Given two sides of a triangle, $\begin{array}{r}a\end{array}$  and $\begin{array}{r}b\end{array}$  (where $\begin{array}{r}a>b\end{array}$ ), the range of the third side, $\begin{array}{r}c,\end{array}$  is:
  ::给定三角形的两面,a和b(如 a>b),第三面的范围,c,是:

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  $$\begin{array}{r}a-b<c<a+b\end{array}$$

      
  ::a-b <c>a+b

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  Creating Parallelograms
  ::创建平行图

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  To review, a is a quadrilateral (a shape with 4 sides) where the opposite sides are parallel . Opposite sides have equal side lengths and opposite angles have equal measures.
  ::要审查的是,a 是对立面平行的四边形(四面形),对面两边的侧边长度相等,对面的角具有等量措施。

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  A rectangle is a parallelogram with four congruent angles and a square is a rectangle with four congruent sides. A square is a rectangle, but a rectangle is not always a square.
  ::矩形是具有四个相容角度的平行图,方形是四个相近边的矩形。方形是一个矩形,四个相近边是正方形。方形是一个矩形,但矩形并不总是正方形。

  	This figure is a parallelogram.  Opposite sides are marked parallel with the arrows. Notice that the different number of arrows is used to mark each set of parallel sides.
  	This figure is a rectangle. In addition, to having  parallel and congruent opposite sides, a ll four angles are congruent and  measure  90°. The small square within each angle is the marking for right angles.
  	T his is a square. In addition to having four congruent angles, the tick-marks indicate that all  four sides are congruent.

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  A diagonal  of any quadrilateral or polygon connects two vertices that are not adjacent (next to each other).  Quadrilaterals   have  two diagonals .
  ::任何四边形或多边形的对角形连接不相邻的两个顶部(彼此相邻)。四边形有两个对角形。

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  To label a triangle, use  a small triangle symbol in front of the three letters. The order will not matter. For a quadrilateral, make sure to list  the vertices in order: start from any vertex and list the vertices as you go around the shape in either direction (clockwise or counterclockwise).
  ::要标签三角形,请在三个字母前使用一个小三角符号。对于四边形,顺序不重要。对于四边形,请确保按顺序列出顶点:从任何顶点开始,并在形状左右方向(按时或按时)列出顶点。

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  In this interactive, you are going to construct a parallelogram with the given properties:
  ::在此交互式互动中, 您将用给定属性构建一个平行图 :

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  • The vertices are  $\begin{array}{r}M,A,T,H,\end{array}$  but not necessarily in that order.
    ::脊椎是M,A,T,H, 但不一定按这个顺序排列。
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  • $\begin{array}{r}\overline{HT}||\overline{MA}\end{array}$  and  $\begin{array}{r}\overline{MH}||\overline{AT}\end{array}$
    ::HT马和MHAT
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  • $\begin{array}{r}MH=2\end{array}$  and  $\begin{array}{r}MA=4\end{array}$  
    ::MH=2和MA=4
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  • No right angles
    ::无右角度
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  • A  fifth point ,  $\begin{array}{r}E,\end{array}$  on  $\begin{array}{r}\overline{MA}\end{array}$  such that  $\begin{array}{r}ME=EA.\end{array}$  
    ::第五点,E,关于MA, 如此的ME=EA。

   

   

   

  arallelograms" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f4574c22ba9708df739fa17&collectionHandle=geometry&collectionCreatorID=3&conceptCollectionHandle=geometry-:arallelograms&mode=lite" test-id="5f4574c22ba9708df739fa17">

   

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  Discussion Question
  ::讨论问题

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  Could you draw more than one parallelogram with the same dimensions as the one in the interactive? Could the parallelogram be a rectangle? 
  ::您能否绘制一个以上的平行图, 其尺寸与交互式图的尺寸相同? 平行图是否是一个矩形 ?

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     Summary
  ::摘要

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  • A triangle is an enclosed geometric figure made up of three line segments and three angles.
    ::三角形是一个封闭的几何数字,由三个线段和三个角度组成。
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  • Two figures are congruent if their measurements are equal. If shapes are congruent, their corresponding measurements are equal.
    ::如果测量结果相等,两个数字是相同的。如果形状是相同的,则相应的测量结果是相等的。
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  • The third side length of a triangle must be between ( but  not equal to) the sum and difference of  the other two side lengths.
    ::三角形的第三侧长度必须介于(但不等于)其他两侧长度之和和和差之间(但不等于)。

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  • A quadrilateral is an enclosed geometric figure made up of four line segments and four angles.
    ::一个四边形是一个封闭的几何数字,由四个线段和四个角度组成。
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  • A parallelogram is a quadrilateral  where opposite sides are parallel.
    ::平行图是一个四边形,对立面是平行的。
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  • A rectangle is a parallelogram where all four angles are right angles.
    ::矩形是一个平行图,所有四个角度都是右角度。
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  • A square is a rectangle where all four sides are equal.
    ::方形是四面平等的一个矩形。
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  • The diagonal of a quadrilateral connects two vertices that are not adjacent.
    ::四边形的对角连接两个不相邻的顶点。