5.3 独特三角-interactive
章节大纲
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In This Lesson
::在本课程中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 。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 。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 。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。
Two Sides and an Included Angle
::双面和包含的角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 。INTERACTIVETwo Sides Including an Angle-
Drag the points to set two of the sides and an included angle of triangles based on the given measurements.
::根据给定的测量结果,拖曳点以设置两边和包括的三角角。 -
Click the button to check your triangle.
::单击按钮检查您的三角形。 -
Answer the question by clicking the dropdown menu.
::点击下拉菜单回答问题。
+Do you want to reset the PLIX?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 。
Two Angles and a Side
::两个角度和一个侧角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 。INTERACTIVETwo Angles Including a Side-
Drag the points to set two angles of triangles based on the given measurements.
::根据给定的测量,拖曳点将设置三角形的两个角度。 -
Click the button to check your triangle.
::单击按钮检查您的三角形。 -
Answer the question by clicking the dropdown menu.
::点击下拉菜单回答问题。
+Do you want to reset the PLIX?roofs-involving-triangles" quiz-url="https://www.ck12.org/assessment/ui/embed.html?test/view/5f45744913dcfe35b8bfd78e&collectionHandle=geometry&collectionCreatorID=3&conceptCollectionHandle=geometry-: roofs-involving-triangles&mode=lite" test-id="5f45744913dcfe35b8bfd78e">
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 。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。
Two Sides and a Not Included Angle
::双侧和未包含的角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 。INTERACTIVETwo Sides and a Not Included Angle-
Drag the red point to adjust the included angle of two sides and form as many triangles as you can.
::拖曳红色点以调整包括的两边角度,并形成尽可能多的三角形。 -
Press the buttons to change the length of one of the sides.
::按下按钮以改变侧边之一的长度 。 -
Displayed values are rounded to the nearest hundredths.
::显示的数值四舍五入到最接近的百分百。
+Do you want to reset the PLIX?Discussion Question
::讨论问题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 ?Summary
::摘要A unique triangle will be produced if you are given:
::如果给定, 将生成一个独有的三角形 :-
all three sides (Side-Side-Side)
::三面三面,三面三面三面,三面三面三面三面三面三面,三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面三面 -
two sides and the included angle (Side-Angle-Side)
::双侧和包含角( 双角- 角度- 斜角) -
two angles and the included side (Angle-Side-Angle)
::两个角度和包含的侧面( 角度- 角度- 角度- 角度)
If you are given all three angles (and no sides), several triangles can be produced of varying sizes.
::如果给您给出了所有三个角度( 没有边边), 几个三角形可以生成不同大小的三角形 。If you are given two sides and a non-included angle , 0, 1 or 2 triangles can be produced.
::如果给您提供两面和一个未包含角度,则可以生成0、1或2个三角形。 -
Drag the points to set two of the sides and an included angle of triangles based on the given measurements.
