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  • 三角形建设

    In This Lesson
    ::在本课程中

    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 。

    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。

    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。

     

    Three Sides
    ::三面

    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 。

     

     

     

     

    Discussion Question
    ::讨论问题

    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 。

     

    Any Three?
    ::有3个吗?

    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 ?

    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 。

     

     

     

     

    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。

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

    a − b < c < a + b
        
    ::a-b <c>a+b

    Creating Parallelograms
    ::创建平行图

    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。

    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。

    A parallelogram showing opposite sides marked with different arrow styles to indicate parallelism.

    		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.

    A rectangle with right angle markings on each corner, illustrating its properties.

    		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.

    An interactive square demonstrating properties of quadrilaterals and how to construct parallelograms.

    		T his is a square. In addition to having four congruent angles, the tick-marks indicate that all  four sides are congruent.

    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。

    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。

    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 :

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

     

     

     

     

    Discussion Question
    ::讨论问题

    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 ?

       Summary
    ::摘要

    • 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。
    • 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。
    • 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)。
    • 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。
    • 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。
    • 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。
    • A square is a rectangle where all four sides are equal.
      ::方形是四面平等的一个矩形。
    • 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。