章节大纲

  • lesson content

    Jurnee wants to make a new sail for her father's sailboat. She finds the old sketch that she used to make the first sail and she redraws the sketch so that she can make the new sail. She uses inches as her scale for the figures, but she plans to use feet when she makes the actual sail. Her two figures are similar.
    ::Jurnee想为她父亲的帆船做新的帆船。她找到了她用来做第一个帆船的旧草图,她重画了草图,这样她就可以做新的帆。她用英寸作为数字的尺码,但她计划当她实际航行时用脚。她的两个数字相似。

    lesson content

    How can Jurnee use a proportion to decide the length of  K J ¯  in inches?
    ::Junie如何用比例来决定 KJ英寸的长度?

    In this concept, you will learn how to use proportions to figure out the length of a missing side.
    ::在这个概念中,你将学会如何使用比例来计算缺失方的长度。

    Calculating Unknown Measures in Similar Figures
    ::以类似数字计算未知计量

    You can write ratios to compare the lengths of sides.
    ::您可以在侧边长度上进行比对。

    lesson content

    First, identify the corresponding sides of these two similar triangles, then place the first side in the numerator and the corresponding side in the denominator.
    ::首先,确定这两个类似三角形的相应侧面,然后将第一侧放在分子中,将相应侧放在分母中。

    L M O P = L N O Q = M N P Q

    These ratios are written in a proportion or a set of three equal ratios. Remember that there is a relationship between the corresponding sides because they are parts of similar triangles. The side lengths of the similar triangles form a proportion.
    ::这些比例以比例或三对等比例来表示。 记住, 对应的两边之间存在某种关系, 因为它们是相似三角形的一部分。 类似三角形的侧长构成一个比例 。

    Let’s substitute the given measurements into the formula.
    ::让我们将给定的测量值换成公式。

    6 3 = 8 4 = 4 2

    There is a pattern with the ratios of corresponding sides. You can see that the measurement of each side of the first triangle divided by two is the measure of the corresponding side of the second triangle.
    ::对应边的比重有一个模式。 您可以看到第一个三角形的每个边除以 2 是第二个三角形的对应边的度量 。

    Use patterns like this to problem solve the length of missing sides of similar triangles.
    ::使用这种模式来解决类似三角形的缺失边的长度问题 。

    lesson content

    These are two similar triangles because they have the same shape but a different size. Therefore, the corresponding sides are similar.
    ::它们是两个相似的三角形, 因为它们的形状相同, 但大小不同。 因此, 相应的边是相似的 。

    If you look at the side lengths, you should see that there is one variable. That is the missing side length. You can figure out the missing side length by using proportions because the corresponding side lengths form a proportion. Let’s write ratios that form a proportion and find the pattern to figure out the length of the missing side.
    ::如果您查看侧边长度, 您应该看到有一个变量。 这是缺失的侧长度。 您可以使用比例来计算缺失的侧长度, 因为相应的侧长度形成比例 。 让我们来计算一个比例的写法比率, 并找到模式来计算缺失的侧长度 。

    A B D E = A C D F = B C E F 5 10 = 15 x = 10 20

    Looking at this you can see the pattern. The side lengths of the second triangle are double the length of the corresponding side of the first triangle.
    ::您可以在此看到图案。 第二个三角形的侧边长度是第一个三角形对应侧长度的两倍 。

    Using this pattern, you can see that the length of  D F  in the second triangle will be twice the length of  A C . The length of  A C  is 15.
    ::使用此模式, 您可以看到第二个三角形的 D F 长度是 A C 长度的两倍。 A C 长度是 15 。

    15  ×  2  =  30

    The length of  D F  is 30.
    ::DF长度为30。

    Examples
    ::实例

    Example 1
    ::例1

    Earlier, you were given a problem about Jurnee and the sail.
    ::早些时候,你遇到了一个问题 关于朱尔尼和帆。

    She wants to make a new sail for her father. She uses an old sketch and makes a new sketch that is similar.
    ::她想为她父亲换条新船 她用旧的草图画出一幅相似的新草图

    lesson content

    How can Jurnee decide the length of    K J ¯   in inches?

    ::Junie如何决定KJ英寸的长度?

    First, use the corresponding sides to set up a proportion.
    ::首先,利用对应方确定比例。

    K J ¯ 5 = 6 4
    ::K J = 5 = 6 4

    Next, use cross products.
    ::接下来,使用交叉产品。

    K J ¯ × 4 = 4 K J ¯ 5 × 6 = 30 4 K J ¯ = 30
    ::K J = 4 = 4 K J = 5 = 6 = 30 4 K J = 30

    Then, solve for    K J ¯ .
    ::那么,解决KJ。

    30 ÷ 4 = 7.5 K J ¯ = 7.5
    ::30 = 4 = 7.5 K J = 7.5

    The answer is that  K J ¯ = 7.5  cm.
    ::答案是KJ=7.5厘米

    Example 2
    ::例2

    Solve for the missing value.
    ::解决丢失的值 。

    8 10 = 4 5 = 2 x
    ::8 10 = 4 5 = 2 x

    First, identify the pattern.
    ::首先,确定模式。

    The denominator is the numerator divided by 0.8.
    ::分母是分子除以0.8。

    Next, set up an equation to solve for  x .
    ::下一个,设置一个方程式来解决 x 。

      2 0.8 = x
    ::2.0.0.8=x

    Then, solve for  x .
    ::然后,解决x。

      x = 2.5
    ::x=2.5x=2.5

    The answer is that  x = 2.5 .
    ::答案是x=2.5。

    Example 3
    ::例3

    Solve for the missing value.
    ::解决丢失的值 。

    6 12 = x 24 = 3 6
    ::6 12 =x 24 = 3 6

    First, identify the pattern.
    ::首先,确定模式。

    The denominator is twice the size of the numerator.
    ::分母是分子大小的两倍。

    Next, set up an equation to solve for  x .
    ::下一个,设置一个方程式来解决 x 。

      24 = 2 × x
    ::24=2xxxx 24=2xxx

    Then, solve for  x .
    ::然后,解决x。

      24 2 = x = 12
    ::24 2 = x = 12

    The answer is that  x = 12 .
    ::答案是 x = 12 。

    Example 4
    ::例4

    Solve for the missing value.
    ::解决丢失的值 。

    12 x = 16 4 = 20 5
    ::12 x = 16 4 = 20 5

    First, identify the pattern.
    ::首先,确定模式。

    The denominator is the result of dividing the numerator by 4.
    ::分母是分子除以 4 的结果。

    Next, set up an equation to solve for  x .
    ::下一个,设置一个方程式来解决 x 。

      12 4 = x
    ::12 4 =xx

    Then, solve for  x .
    ::然后,解决x。

      x = 3
    ::x=3x=3

    The answer is that  x = 3 .
    ::答案是 x = 3 。

    Example 5
    ::例5

    Solve for the missing value.
    ::解决丢失的值 。

    8 2 = 16 4 = x 1
    ::8 2 = 16 4 = x 1

    First, identify the pattern.
    ::首先,确定模式。

    The denominator is the result of dividing the numerator by 4.
    ::分母是分子除以 4 的结果。

    Next, set up an equation to solve for  x .
    ::下一个,设置一个方程式来解决 x 。

      x 4 = 1
    ::x 4 = 1

    Then, solve for  x .
    ::然后,解决x。

      x = 4 × 1 = 4
    ::x = 4x 1 = 4

    The answer is that  x = 4 .

    ::答案是 x = 4 。

    Review
    ::回顾

    Use the following ratio to answer the questions.
    ::使用以下比例回答问题。

    7 3.5 = x 3.5 = 6 y

    1. What is value of  x ?  
      ::x 值是什么?
    2. What is value of  y ?
      ::y的价值是什么?
    3. How did you figure these out?
      ::你怎么知道这些的?

    Figure out the missing value in each pair of ratios.
    ::找出每一对比率的缺失值。

    1. 6 12 = x 24
      ::6 12 =x 24
    2. 8 12 = x 3
      ::8 12 = x 3
    3. 9 10 = 18 y
      ::9 10 = 18 y
    4. 4 5 = x 2.5
      ::4 5 = x 2.5
    5. 16 20 = 4 y
      ::16 20 = 4 y
    6. 19 21 = x 42
      ::19 21 = x 42
    7. 9 54 = 6 y
      ::9 54 = 6 y

    Review (Answers) 
    ::回顾(答复)

    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 。

    Resources
    ::资源