Course: 6.3 标明线条类型

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标明线条类型
Candice saw the following illustration in her m ath book.
::Candice在其数学书中看到以下插图。

She wondered how to describe the relationship between the brown plane and the green plane.
::她想知道如何描述棕色平面与绿色平面之间的关系。

In this concept, you will learn to identify types of lines.
::在此概念中,您将学会辨别线条的类型。

Parallel, Perpendicular and Intersecting Lines
::平行线、垂直线和交叉线

Lines are around you everywhere and you see them every day. When you drive along a highway there are lines painted on the road indicating the width of the lane, lines painted indicating cross walks and lines indicating the intersection of roads. If you look up to the sky you often see lines that are vapor trails left by airplanes.
::横线环绕着你们四周,每天都能看到。当你沿着高速公路行驶时,路面上涂有标明车道宽度的线条,画有标明横行的线条和标明路交汇处的线条。如果你仰望天空,你经常看到飞机留下的蒸发痕迹。

Although lines are a common occurrence in the real-world, they are special and have names. The lines painted on the road indicating the width of the driving lane are parallel lines . Parallel lines are two lines on a plane that never meet and remain the same distance over their entire length. The following diagrams show pairs of parallel lines:
::虽然线路在现实世界中是常见的,但它们是特别的,并有名称。在路上绘制的标明车道宽度的线路是平行线。平行线是飞机上的两条线,从不相遇,并且在整个长度上保持同样的距离。下图显示了两条平行线:

The arrows on the lines show that the lines are parallel to each other. When naming lines that are parallel, the symbol $\begin{aligned} ∥ \end{aligned}$ is used.
::线条上的箭头显示线条是平行的。当命名平行的线条时,使用符号。

Straight lines that are at right angles to each other are called perpendicular lines . These lines meet each other such that a 90° angle is formed. When a Cartesian grid is drawn, the $\begin{aligned} x \end{aligned}$ and $\begin{aligned} y \end{aligned}$ axes meet at right angles. When naming lines that are perpendicular , the symbol $\begin{aligned} ⊥ \end{aligned}$ is used.
::直线直线直角直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线直线

Straight lines that cross each other at some point are called intersecting lines . These lines will intersect at one point only over their entire length. There is no symbol to use when naming intersecting lines. The following diagram shows intersecting lines.
::在某个点上相互交错的直线被称作交叉线。这些直线将仅在整个长度的一个点上交叉。在命名交叉线时没有符号可以使用。下图显示交叉线。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Candice and the picture. She needs to describe the relationship between the two planes.
::早些时候,有人给了你Candice和照片的问题。她需要描述两架飞机之间的关系。

First, look at the two planes and write down what she knows from the picture.
::首先,看看这两架飞机写下她从照片中知道的东西

The green plane and the brown plane are equidistant – the distance between them is equal over their entire length.
::绿色平面与棕色平面的距离相当,

Next, figure out what this means with respect to the planes.
::接下来,找出这对飞机意味着什么。

This means that the planes will never meet or intersect.
::这意味着飞机永远不会相遇或交叉。

Then, state the relationship between the planes.
::然后说说飞机之间的关系

The planes are parallel.
::飞机是平行的

Candice can now say that the green and brown planes in the picture are parallel.
::Candice现在可以说照片中的绿色和棕色飞机是平行的

Example 2
::例2

Name the type of lines represented by the following real-world situations:
::命名由下列现实世界局势代表的线条类型:

i) Railroad tracks and overhead power lines.
:一) 铁路轨道和高架电线。

ii) Diagonal distances from home plate to 2 ^nd base and from 1 ^st base to 3 ^rd base of a baseball diamond.
:二) 从家用车牌到第二基地的对角距离,以及从棒球钻石第一基地到第三基地的对角距离。

iii) Solid double lines painted in the middle of a two-way road.
:三) 在双向公路中间漆的固体双线。

iv) Corners formed by the trim around a rectangular window.
:四) 矩形窗口周围的圆形形成的角。

v) Legs of an ironing board
:五) 熨烫板的脚

Answers:
::答复:

i) Railroad tracks and overhead power lines.
:一) 铁路轨道和高架电线。

Parallel lines.
::平行线条。

ii) Diagonal distances from home plate to 2 ^nd base and from 1 ^st base to 3 ^rd base of a baseball diamond.
:二) 从家用车牌到第二基地的对角距离,以及从棒球钻石第一基地到第三基地的对角距离。

Perpendicular lines.
::直肠直线

iii) Solid double lines painted in the middle of a two-way road.
:三) 在双向公路中间漆的固体双线。

Parallel lines.
::平行线条。

iv) Corners formed by the trim around a rectangular window.
:四) 矩形窗口周围的圆形形成的角。

Perpendicular lines.
::直肠直线

v) Legs of an ironing board.
:五) 熨衣板的脚。

Intersecting lines
::交叉线

Example 3
::例3

For the following regular trapezoid name, with proper symbols, one pair of parallel lines, one pair of intersecting lines and one pair of perpendicular lines.
::对于以下具有适当符号的普通孔雀类名称、一对平行线、一对交叉线和一对垂直线。

Parallel Lines
::平行线线

First, review what you know about parallel lines.
::首先,回顾你对平行线的了解。

-always the same distance apart
::- 相隔距离总是一样的距离

-never meet or intersect
::- 从未相遇或交叉

-indicated with same arrows on the lines
::- 直线上的箭头相同

Next, look at the diagram and find the pair of parallel lines
::下一个,看看图表,找到平行线条

Lines $\begin{aligned} \bar{A B} \end{aligned}$ and $\begin{aligned} \bar{C D} \end{aligned}$ display an arrow.
::线 AB 和 CD 显示箭头。

Then, name the parallel lines using the correct symbol.
::然后用正确的符号命名平行线条。

$\begin{aligned} \bar{A B} ∥ \bar{C D} \end{aligned}$
::AB - 来啦 - 来啦 - 来啦 - 来啦 - 来啦

Intersecting Lines
::交叉线

First, review what you know about intersecting lines.
::首先,审查你对交叉线的了解。

-intersect at one point only
::- 仅在一个点相交

-can intersect at any angle
::- 以任何角度相交叉

-no indication marks
::- 无指示标记

Next, look at the diagram and find the pair of intersecting lines.
::接下来,看看图表,找到两条交叉线。

$\begin{aligned} \bar{A D} \end{aligned}$ and $\begin{aligned} \bar{B C} \end{aligned}$
::和BCA和BC

Then, name the intersecting lines using the correct symbol.
::然后用正确的符号命名交叉线。

$\begin{aligned} \bar{A D} \end{aligned}$ intersects $\begin{aligned} \bar{B C} \end{aligned}$ . There is no symbol to represent intersecting lines
::没有符号代表交叉线条

Perpendicular Lines
::直直直线

First, review what you know about perpendicular lines.
::首先,审查你对垂直线的了解。

-intersect or meet at one point only
::- 相交或只碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰碰

-will meet or intersect at a 90° angle
::- 将在90度角相撞或交叉

- right angle is shown with a square
::- 右角度以正方形显示

Next, look at the diagram and find the pair of intersecting lines.
::接下来,看看图表,找到两条交叉线。

$\begin{aligned} \bar{A E} \end{aligned}$ and $\begin{aligned} \bar{C D} \end{aligned}$
::AE和CD

Then, name the intersecting lines using the correct symbol.
::然后用正确的符号命名交叉线。

$\begin{aligned} \bar{A E} ⊥ \bar{C D} \end{aligned}$ .
::AE 来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来,来

Review
::回顾

Name each type of lines shown below.
::列出下列每一类型的行。

1.

2.

3.

4.

Write the definitions for the following types of lines.
::4. 为以下几行编写定义。

5. Parallel lines
::5. 平行线

6. Intersecting lines
::6. 交叉线

7. Perpendicular lines
::7. 垂直直直线

Answer the following questions about different types of lines.
::回答以下关于不同类型线条的问题。

8. What is the symbol for parallel lines?
::8. 平行线的符号是什么?

9. What is the symbol for perpendicular lines?
::9. 垂直线的符号是什么?

10. An intersection on a highway is an example of what type of lines?
::10. 公路上的交叉路口是哪一类线路的例子?

11. A four way stop at a {90}^{\circ} is an example of what type of lines?
::11. 在{90circ}的四条路停留是哪一类线的一个例子?

12. Is it possible for intersecting lines to also be considered perpendicular?
::12. 是否还可以将交叉线也视为垂直线?

Describe the types of lines shown in each illustration.
::描述每个插图中显示的线条类型。

13.

14.

15.

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

Section outline

General

标明线条类型

Parallel, Perpendicular and Intersecting Lines ::平行线、垂直线和交叉线

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Parallel, Perpendicular and Intersecting Lines
::平行线、垂直线和交叉线

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源