Course: 1.6 角分类 | The Way To Learn

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角度分类分类
Classifying Angles
::分类分类角度

Angles can be grouped into four different categories.
::角可以分为四大类。

Straight Angle : An angle that measures exactly $\begin{aligned} 180^{\circ} \end{aligned}$ .
::直角 : 精确测量 180 的角。

Acute Angles : Angles that measure between $\begin{aligned} 0^{\circ} \end{aligned}$ and up to but not including $\begin{aligned} 90^{\circ} \end{aligned}$ .
::急性角:测量 0至最高但不包括 90之间的角。

Obtuse Angles: Angles that measure more than $\begin{aligned} 90^{\circ} \end{aligned}$ but less than $\begin{aligned} 180^{\circ} \end{aligned}$ .
::阻力角: 测量超过 90 的角, 但小于 180 的角。

Right Angle : An angle that measures exactly $\begin{aligned} 90^{\circ} \end{aligned}$ .
::右角: 精确测量 90 的角。

This half- square marks right, or $\begin{aligned} 90^{\circ} \end{aligned}$ , angles. When two lines intersect to form four right angles, the lines are perpendicular . The symbol for perpendicular is $\begin{aligned} ⊥ \end{aligned}$ .
::这个半平方标记右转, 或 90 , 角度。当两条线交叉形成四个右角时, 直线是垂直的。直线的符号是。

Even though all four angles are $\begin{aligned} 90^{\circ} \end{aligned}$ , only one needs to be marked with the half-square. $\begin{aligned} l ⊥ m \end{aligned}$ is read line $\begin{aligned} l \end{aligned}$ is perpendicular to line $\begin{aligned} m \end{aligned}$ .
::尽管所有四个角度都是90,但只需用半平方标记一个。Im读行I与m直线垂直。

What if you were given the degree measure of an angle? How would you describe that angle based on its size?
::如果给您一个角度的度量度呢? 您如何根据角度的大小描述该角度 ?

Examples
::实例

Example 1
::例1

What type of angle is $\begin{aligned} 90^{\circ} \end{aligned}$ ?
::90是哪种角度?

The angle measure is exactly $\begin{aligned} 90^{\circ} \end{aligned}$ , so it is right.
::角度量度正好是90,所以是正确的。

Example 2
::例2

What type of angle is $\begin{aligned} 84^{\circ} \end{aligned}$ ?
::84是什么样的角度?

$\begin{aligned} 84^{\circ} \end{aligned}$ is less than $\begin{aligned} 90^{\circ} \end{aligned}$ , so it is acute.
::84小于90,所以是急性。

Example 3
::例3

What type of angle is $\begin{aligned} 165^{\circ} \end{aligned}$ ?
::165是哪种角度?

$\begin{aligned} 165^{\circ} \end{aligned}$ is greater than $\begin{aligned} 90^{\circ} \end{aligned}$ , but less than $\begin{aligned} 180^{\circ} \end{aligned}$ , so it is obtuse.
::165比90还大,但小于180,所以是模糊的。

Example 4
::例4

Name the angle and determine what type of angle it is.
::命名角度并确定是哪种角度。

The vertex is $\begin{aligned} U \end{aligned}$ . So, the angle can be $\begin{aligned} ∠ T U V \end{aligned}$ or $\begin{aligned} ∠ V U T \end{aligned}$ . To determine what type of angle it is, compare it to a right angle.
::顶点是 U。所以, 角度可以是 TUV 或 VUT 。要确定是哪种角度, 请将其与右角度比较。

Because it opens wider than a right angle and is less than a straight angle, it is obtuse .
::因为它打开的宽度大于一个右角度, 也小于一个直角, 它就是模糊的。

Review
::回顾

For exercises 1-4, determine if the statement is true or false.
::练习 1-4 确定声明是真实的还是虚假的。

Two angles always add up to be greater than $\begin{aligned} 90^{\circ} \end{aligned}$ .
::两个角度加起来总大于90。

$\begin{aligned} 180^{\circ} \end{aligned}$ is an obtuse angle.
::180是个隐蔽的角度

$\begin{aligned} 180^{\circ} \end{aligned}$ is a straight angle.
::180是直角

Two perpendicular lines intersect to form four right angles.
::两条垂直直线交叉,形成四个右角。

For exercises 5-10, state what type of angle it is.
::对于演习5-10,请说明是何种角度。

$\begin{aligned} 55^{\circ} \end{aligned}$

$\begin{aligned} 92^{\circ} \end{aligned}$

$\begin{aligned} 178^{\circ} \end{aligned}$

$\begin{aligned} 5^{\circ} \end{aligned}$

$\begin{aligned} 120^{\circ} \end{aligned}$

$\begin{aligned} 73^{\circ} \end{aligned}$

In exercises 11-15, use the following information: $\begin{aligned} Q \end{aligned}$ is in the interior of $\begin{aligned} ∠ R O S \end{aligned}$ . $\begin{aligned} S \end{aligned}$ is in the interior of $\begin{aligned} ∠ Q O P \end{aligned}$ . $\begin{aligned} P \end{aligned}$ is in the interior of $\begin{aligned} ∠ S O T \end{aligned}$ . $\begin{aligned} S \end{aligned}$ is in the interior of $\begin{aligned} ∠ R O T \end{aligned}$ and $\begin{aligned} m ∠ R O T = 160^{\circ}, m ∠ S O T = 100^{\circ} \end{aligned}$ , and $\begin{aligned} m ∠ R O Q = m ∠ Q O S = m ∠ P O T \end{aligned}$ .
::在11-15演习中,请使用以下信息:Q在QROS内地;S在QOP内地;P在QSOT内地;S在QROT内地;MZOT=160;MQSOT=100;和MQROmOS=mPOT。

Make a sketch.
::做一个草图。

Find $\begin{aligned} m ∠ Q O P \end{aligned}$ .
::去找妈妈

Find $\begin{aligned} m ∠ Q O T \end{aligned}$ .
::找妈妈。

Find $\begin{aligned} m ∠ R O Q \end{aligned}$ .
::去找麦奎克

Find $\begin{aligned} m ∠ S O P \end{aligned}$ .
::找到MSOP。

Review (Answers)
::回顾(答复)

To see the Review answers, open this and look for section 1.6.
::阅读《评论》的答复,打开这个打开,看看第1.6节。

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。

Section outline

General

角度分类分类

Classifying Angles ::分类分类角度

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Review ::回顾

Review (Answers) ::回顾(答复)

Review (Answers) ::回顾(答复)

Classifying Angles
::分类分类角度

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Review
::回顾

Review (Answers)
::回顾(答复)

Review (Answers)
::回顾(答复)