Course: 3.4 替代内地角 | The Way To Learn

Section outline

Select section General

Collapse Expand
General

Collapse all Expand all
- Select activity 新闻通告
  
  新闻通告 Forum
Select section 替代内部角

Collapse Expand
替代内部角
Alternate Interior Angles
::替代内部角

Alternate interior angles are two angles that are on the interior of $\begin{aligned} l \end{aligned}$ and $\begin{aligned} m \end{aligned}$ , but on opposite sides of the transversal .
::交替内角是I和M内部的两个角度,但横向两侧。

Alternate Interior Angles Theorem : If two parallel lines are cut by a transversal, then the alternate interior angles are congruent .
::替代内部角定理 : 如果两条平行线被横切切开, 那么其它内部角度是相似的。

If $\begin{aligned} l | | m \end{aligned}$ , then $\begin{aligned} ∠ 1 ≅ ∠ 2 \end{aligned}$
::如果lm,那么12

Converse of Alternate Interior Angles Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel .
::反之, 替代内地定理 : 如果两条线由横向线切开, 而其它内部角度是相似的, 那么线是平行的。

If then $\begin{aligned} l | | m \end{aligned}$ .
::如果那样的话

What if you were presented with two angles that are on the interior of two parallel lines cut by a transversal but on opposite sides of the transversal? How would you describe these angles and what could you conclude about their measures?
::如果有人向你们展示两条平行线内侧的两个角度,这两条平行线由横跨的但横跨的两条线截断的两条平行线的内侧,你们将如何描述这些角度,以及你们能得出什么结论呢?

Examples
::实例

For Examples 1 and 2, use the given information to determine which lines are parallel. If there are none, write none. Consider each question individually.
::对于例1和例2,使用给定的信息来确定哪些线条是平行的。如果没有,请写无。逐个考虑每个问题。

Example 1
::例1

$\begin{aligned} ∠ E A F ≅ ∠ F J I \end{aligned}$
::斐济

None
::无无无无无无无

Example 2
::例2

$\begin{aligned} ∠ E F J ≅ ∠ F J K \end{aligned}$
::EFJ*FJK(欧洲儿童基金)

$\begin{aligned} \overset{\leftrightarrow}{C G} | | \overset{\leftrightarrow}{H K} \end{aligned}$
::CGHK

Example 3
::例3

Find the value of $\begin{aligned} x \end{aligned}$ .
::查找 x 的值。

The two given angles are alternate interior angles and equal.
::给定的两个角度是不同的内部角度和相等的角。

$\begin{aligned} (4 x - 10)^{\circ} & = 58^{\circ} \\ 4 x & = 68 \\ x & = 17 \end{aligned}$

:4x-10)584x=68x=17)

Example 4
::例4

True or false: alternate interior angles are always congruent.
::真实的或假的: 其它内部角度总是一致的。

This statement is false, but is a common misconception. Remember that alternate interior angles are only congruent when the lines are parallel.
::此语句是虚假的, 但是一个常见的错误概念。请记住, 其它内部角度只有在线条平行时才一致。

Example 5
::例5

What does $\begin{aligned} x \end{aligned}$ have to be to make $\begin{aligned} a | | b \end{aligned}$ ?
::X 需要做什么才能做 ab ?

The angles are alternate interior angles, and must be equal for $\begin{aligned} a | | b \end{aligned}$ . Set the expressions equal to each other and solve.
::角度是不同的内部角度, a+++b 必须是相等的。设置对齐的表达式并解析。

$\begin{aligned} 3 x + 16^{\circ} & = 5 x - 54^{\circ} \\ 70 = 2 x \\ 35 = x \end{aligned}$

::3x+165x-5470=2x35=x

To make $\begin{aligned} a | | b, x = 35 \end{aligned}$ .
::做 ab, x=35。

Review
::回顾

Is the angle pair $\begin{aligned} ∠ 6 \end{aligned}$ and $\begin{aligned} ∠ 3 \end{aligned}$ congruent, supplementary or neither?
::角度对 6 和 3 是否一致, 补充还是两者兼而有之?

Give two examples of alternate interior angles in the diagram:
::在图表中举两个替代内部角度的例子 :

For 3-4, find the values of $\begin{aligned} x \end{aligned}$ .
::3 -4,找到x的值。

For question 5, use the picture below. Find the value of $\begin{aligned} x \end{aligned}$ .
::对于问题5, 请使用下面的图片。查找 x 的值。

$\begin{aligned} m ∠ 4 = (5 x - 33)^{\circ}, m ∠ 5 = (2 x + 60)^{\circ} \end{aligned}$
::m*4=(5x-33) , m*5=(2x+60)

Are lines $\begin{aligned} l \end{aligned}$ and $\begin{aligned} m \end{aligned}$ parallel? If yes, how do you know?
::l线和m线平行吗?如果是,你怎么知道?

For 7-10, what does the value of $\begin{aligned} x \end{aligned}$ have to be to make the lines parallel?
::对于7-10,x的值是多少才能使线平行?

$\begin{aligned} m ∠ 4 = (3 x - 7)^{\circ} \end{aligned}$ and $\begin{aligned} m ∠ 5 = (5 x - 21)^{\circ} \end{aligned}$
::m*4=( 3x-7) *和 m*5=( 5x- 21) * *

$\begin{aligned} m ∠ 3 = (2 x - 1)^{\circ} \end{aligned}$ and $\begin{aligned} m ∠ 6 = (4 x - 11)^{\circ} \end{aligned}$
::3=( 2x-1) (4x- 11)

$\begin{aligned} m ∠ 3 = (5 x - 2)^{\circ} \end{aligned}$ and $\begin{aligned} m ∠ 6 = (3 x)^{\circ} \end{aligned}$
::3=( 5x-2)

$\begin{aligned} m ∠ 4 = (x - 7)^{\circ} \end{aligned}$ and $\begin{aligned} m ∠ 5 = (5 x - 31)^{\circ} \end{aligned}$
::m4=(x-7)和m5=(5x-31)

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

替代内部角

Alternate Interior Angles ::替代内部角

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Alternate Interior Angles
::替代内部角

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源