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  • General

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  • 高度高度

    Altitudes
    ::高度高度

    In a triangle , a line segment from a vertex and perpendicular to the opposite side is called an altitude . It is also called the height of a triangle. The red lines below are all altitudes.
    ::在三角形中,从顶部和垂直到对面的一条线段称为高度。它也称为三角形的高度。下面的红线是所有高度。

    When a triangle is a right triangle , the altitude, or height, is the leg. If the triangle is obtuse, then the altitude will be outside of the triangle. If the triangle is acute, then the altitude will be inside the triangle.
    ::当三角形是右三角形时, 高度或高度是腿。 如果三角形是模糊的, 高度在三角形之外。 如果三角形是急性的, 高度在三角形之内 。

    What if you were given one or more of a triangle's angle measures? How would you determine where the triangle's altitude would be found?
    ::如果给您一个或数个三角角的度量呢? 您如何确定三角角的高度?

    Examples
    ::实例

    Example 1
    ::例1

    True or false: The altitudes of an obtuse triangle are inside the triangle.
    ::真实的或假的:一个隐形三角的高度在三角内。

    Every triangle has three altitudes. For an obtuse triangle, at least one of the altitudes will be outside of the triangle, as shown in the picture at the beginning of this section.
    ::每个三角形有三个高度。对于一个隐形三角形,至少有一个高度将在三角形之外,正如本节开头的图片所示。

    Example 2
    ::例2

    Draw the altitude for the triangle shown.
    ::为显示的三角形绘制高度。

    The triangle is a right triangle, so the altitude is already drawn. The altitude is X Z ¯ .
    ::三角形是一个右三角形, 所以高度已经绘制。 高度是 XZ 。

    Example 3
    ::例3

    Which line segment is the altitude of △ A B C ?
    ::ABC的高度是哪一线段?

    In a right triangle, the altitude, or the height, is the leg. If we rotate the triangle so that the right angle is in the lower left corner, we see that leg B C ¯ is the altitude.
    ::在右三角形中,高度或高度是腿。如果我们旋转三角形,使右角位于左下角,我们可以看到BC腿是高度。

    Example 4
    ::例4

    A triangle has angles that measure 55 ∘ , 60 ∘ , and 65 ∘ . Where will the altitude be found?
    ::三角形有角度可以测量 55, 60, 65。 高度会在哪里找到 ?

    Because all of the angle measures are less than 90 ∘ , the triangle is an acute triangle . The altitude of any acute triangle is inside the triangle.
    ::由于所有角度量都小于 90 , 三角形是一个尖三角形。 任何尖三角形的高度都在三角形内 。

    Example 5
    ::例5

    A triangle has an angle that measures 95 ∘ . Where will an altitude be found?
    ::三角形的角度可以测量 95\\\\ 。 在哪里可以找到高度 ?

    Because 95 ∘ > 90 ∘ , the triangle is obtuse and it will be outside the triangle.
    ::因为9590, 三角形是模糊的, 并且它将会在三角形之外。

    Review
    ::回顾

    Given the following triangles, tell whether the all three possible altitude is inside the triangle or if an altitude is outside the triangle.
    ::根据以下三角形,请说明三角形内是否有所有三种可能高度,或者三角形外是否有高度。

    6. △ J K L is an equiangular triangle.
      ::jKL是一个等角三角形。
    7. △ M N O is a triangle in which two the angles measure 30 ∘ and 60 ∘ .
      ::@MNO 是一个三角形, 其中两个角度测量 30 和 60 。 @ info: whatsthis
    8. △ P Q R is an isosceles triangle in which two of the angles measure 25 ∘ .
      ::QPQR 是一个等分三角形, 其中两个角度测量 25°C 。
    9. △ S T U is an isosceles triangle in which two angles measures 45 ∘ .
      ::STU是一个等星三角形, 其中两个角度测量 45°C 。

    Given the following triangles, which line segment is a possible altitude?
    ::根据以下三角形,哪一线段是可能的高度?

    1. △ A B C
      ::ABC(ABC)
    2. △ I J K
      ::#IJK # # IJK # # IJK # # IJK # # IJK # # IJK # # IJK #
    3. △ M N O
      ::哦,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不,不
    4. △ R S Q
      ::RSQ( RSQ)
    5. △ U V W
      ::UVW(世界展望组织)

    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