独特三角形

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In This Lesson
::在本课程中

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Y ou will discover ways to construct unique triangles involving the angles .  
::您将找到构建包含角度的独特三角形的方法 。

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T he lesson  discussed  how to make a triangle given three side lengths. As you discovered, as long as two of the lengths added up to be greater than the third, they would form a unique triangle (only one triangle could be formed). It did not matter how you rotated or flipped the triangle because all of the angles would remain the same. 
::课程讨论了如何用三个侧边长度来设置三角形。 正如您所发现的那样, 只要两个长度加起来大于第三个长度, 它们就会形成一个独特的三角形( 只能形成一个三角形 ) 。 您如何旋转或翻转三角形并不重要, 因为所有角度都保持不变 。

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To quickly review how to draw an angle using a protractor , start by drawing a horizontal, straight line . Then, place the protractor's 0° line on it such that the center of the protractor  is on the vertex . Measure the angle and mark it (make sure you are using the correct measurements, there are two numbers listed around the arc of the protractor, depending on which side the angle is facing. See the pictures below.
::要快速查看如何使用减速器绘制角, 首先绘制水平直线。 然后, 将减速器的 0 ° 线放在它上, 使减速器的中心在顶部。 测量角并标记它( 确定您正在使用正确的测量方法, 在减速器弧周围列出两个数字, 取决于角面向的侧面 。 见下面的图片 。

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In addition, the longest side of a triangle is always opposite the largest angle.  Similarly,  the shortest side is always opposite the smallest angle.
::此外,三角形最长的一面总是对着最大的角。 同样,最短的一面总是对着最小的角。

 

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Two Sides and an Included Angle
::双面和包含的角

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If you are given two lengths and an angle between them (called the included angle ) can you produce a unique triangle? In this interactive, you  will be given different sets of two sides with  the included angle. For each set , s ee if more than one triangle can be produced.
::如果给您给出两个长度和两个角度之间的角( 称为包含角度) , 您能够生成一个独特的三角形吗 ? 在此互动中, 您将得到包含角度的不同两边的一组。 对于每一组, 请查看是否可以生成一个以上的三角形 。

 

 

 

 

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You   used side-angle-side , or , to construct the triangles in the interactive.  It is important to note that SAS construction will always produce one, unique triangle. It does not matter how much you flip, rotate or move the triangle, the measurements will not change.  Even though the triangle may "look" different, it still has the same angle measures and side lengths.  The orientation of a shape will never change  the dimensions , just  the placement.
::您在互动中用侧角侧边或 来构造三角形。 必须指出, SAS 构造总是会生成一个独特的三角形。 无论您翻转、 旋转或移动三角形多少, 测量结果都不会改变。 尽管三角形可能“ 看” 不同, 但它仍然有相同的角度度量和侧边长。 形状的方向永远不会改变尺寸, 仅仅是位置 。

 

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Two Angles and a Side
::两个角度和一个侧角

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If you are given two angle measures  and the side between them (called the included side ) can you produce a unique triangle? In this interactive, you  will be given different sets of two angles with the included side. For each set, see if more than one triangle can be produced.
::如果给您两个角度的度量和它们之间的侧面( 称为包含的边) , 您能够生成一个独特的三角形吗 ? 在此互动中, 您将会在包含的侧面上获得不同的两组角度。 对于每组, 看看是否可以生成一个以上的三角形 。

 

 

 

 

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You used angle-side-angle, or ASA , to construct the triangles in the interactive. G iven two angles and the included side, a unique triangle will always be produced. Y ou could find the third angle by subtracting the given two from 180° and then could  construct the triangle using the angles and given side length.  
::您在互动中用角度侧角或 ASA 来构造三角形。 在两个角度和包含的侧面下, 总是会生成一个独特的三角形。 您可以从 180 ° 中减去给定两个角度, 找到第三个角度, 然后用角度和给定的侧长来构造三角形 。

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Next, you will look at what happens when you are  given two sides and a not included angle.  
::接下来,你将观察当你得到两面和一个未包含的角度时会发生什么。

 

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Two Sides and a Not Included Angle
::双侧和未包含的角

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The last case for triangle construction is when you are given two sides and  an angle that is not included. Use this interactive to investigate what happens.
::三角形构造的最后一个实例是您被给定了两面, 角度没有包含。 使用此互动来调查发生了什么 。

 

 

 

 

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Discussion Question
::讨论问题

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The interactives in this lesson were designed to help you derive the properties for unique triangles. Which real life tools could you have used instead? Do you feel the interactives or the physical tools would have been more effective?
::此课中的交互式课程旨在帮助您获取独有三角形的属性。 您可以使用哪种真实生活工具来代替这些工具? 您觉得互动工具或物理工具会更有效吗 ?