Як називається прилад який використовується для вимірювання кутів

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1.9: Вимірювання кутів

Кут утворюється, коли два промені мають однакову кінцеву точку. Вершина є загальною кінцевою точкою двох променів, які утворюють кут. Сторони – це два промені, які утворюють кут. Малюнок \(\PageIndex\)

Позначте цеСкажи це
\(\angle ABC\)Кут \(ABC\)
\(\angle CBA\)Кут \(CBA\)
  1. Почніть з малювання горизонтальної лінії по всій сторінці, довжиною 2 дюйма.
  1. Помістіть кінцеву точку в лівій частині лінії.
  2. Помістіть транспортир на цю точку, таким чином, щоб лінія проходила через \( 0 ^\) мітку на транспортирі, а кінцева точка виявилася в центрі. Відзначте \( 50 ^\) на відповідній шкалі.
  1. Зніміть транспортир і з’єднайте вершину і \(50 ^\) mark.

This process can be used to draw any angle between \(0 ^\) and \(180 ^\) .

When two smaller angles form to make a larger angle, the sum of the measures of the smaller angles will equal the measure of the larger angle. This is called the Angle Addition Postulate. So, if B is on the interior of \(\angle ADC\) , then

\(\angle ADC = m \angle ADB + \angle BDC\)

How many angles are in the picture below? Label each one.

Solution

There are three angles with vertex \(U\) . It might be easier to see them all if we separate them.

So, the three angles can be labeled, ( \(\angle XUY\) or \(\angle YUX\) ), \(\angle YUZ\) (or \(\angle ZUY\) ), and \(\angle XUZ\) (or \(\angle ZUX\) ).

Measure the three angles from Example 1, using a protractor.

Solution

Just like in Example 1, it might be easier to measure these three angles if we separate them.

With measurement, we put an m in front of the \(\angle\) sign to indicate measure. So, \(m \angle XUY = 84^\) , \(m \angle YUZ = 42^\) and \(m \angle XUZ = 126^\) .

What is the measure of the angle shown below?

Solution

This angle is not lined up with 0∘, so use subtraction to find its measure. It does not matter which scale you use, as long as you are consistent.

Use a protractor to measure \(\angle RST\) below.

Solution

Lining up one side with \(0 ^\) on the protractor, the other side hits \(100 ^\) .

What is \(m \angle QRT\) in the diagram below?

Solution

Using the Angle Addition Postulate, \(m\angle QRT = 15^+30^=45^\) .

Review

1. What is \(m \angle LMN\) if \(m \angle LMO = 85^\) and \(m \angle NMO = 53^\) ?

2. If \(m \angle ABD = 100^\) , find \(x\) .

For questions 3-6, determine if the statement is true or false.

  1. For an angle \(\angle ABC\) , \(C\) is the vertex.
  2. For an angle \(\angle ABC\) , \(\overline\) and \(\overline\) are the sides.
  3. The \(m\) in front of \(m \angle ABC\) means measure.
  4. The Angle Addition Postulate says that an angle is equal to the sum of the smaller angles around it.

For 7-12, draw the angle with the given degree, using a protractor and a ruler.

For 13-16, use a protractor to determine the measure of each angle.

  1. Figure \(\PageIndex\)
  2. Figure \(\PageIndex\)
  3. Figure \(\PageIndex\)
  4. Figure \(\PageIndex\)

Review (Answers)

To see the Review answers, open this PDF file and look for section 1.5.

Vocabulary

TermDefinition
AngleA geometric figure formed by two rays that connect at a single point or vertex.
ProtractorA protractor is a tool used to measure an angle in terms of degrees.
VertexA vertex is a point of intersection of the lines or rays that form an angle.

Additional Resource

Video: Angle Basics

Activities: Angle Measurement Discussion Questions

Study Aids: Angles Study Guide

Practice: Measuring Angles

Real World: Angle Measurement

Recommended articles

  1. Article type Section or Page License CK-12 Show Page TOC No on Page
  2. Tags
    1. authorname:ck12
    2. program:ck12
    3. source@https://www.ck12.org/c/geometry
    4. source[translate]-k12-2136

    1.9: Вимірювання кутів

    Кут утворюється, коли два промені мають однакову кінцеву точку. Вершина є загальною кінцевою точкою двох променів, які утворюють кут. Сторони – це два промені, які утворюють кут. Малюнок \(\PageIndex\)

    Позначте цеСкажи це
    \(\angle ABC\)Кут \(ABC\)
    \(\angle CBA\)Кут \(CBA\)
    1. Почніть з малювання горизонтальної лінії по всій сторінці, довжиною 2 дюйма.
    1. Помістіть кінцеву точку в лівій частині лінії.
    2. Помістіть транспортир на цю точку, таким чином, щоб лінія проходила через \( 0 ^\) мітку на транспортирі, а кінцева точка виявилася в центрі. Відзначте \( 50 ^\) на відповідній шкалі.
    1. Зніміть транспортир і з’єднайте вершину і \(50 ^\) mark.

    This process can be used to draw any angle between \(0 ^\) and \(180 ^\) .

    When two smaller angles form to make a larger angle, the sum of the measures of the smaller angles will equal the measure of the larger angle. This is called the Angle Addition Postulate. So, if B is on the interior of \(\angle ADC\) , then

    \(\angle ADC = m \angle ADB + \angle BDC\)

    How many angles are in the picture below? Label each one.

    Solution

    There are three angles with vertex \(U\) . It might be easier to see them all if we separate them.

    So, the three angles can be labeled, ( \(\angle XUY\) or \(\angle YUX\) ), \(\angle YUZ\) (or \(\angle ZUY\) ), and \(\angle XUZ\) (or \(\angle ZUX\) ).

    Measure the three angles from Example 1, using a protractor.

    Solution

    Just like in Example 1, it might be easier to measure these three angles if we separate them.

    With measurement, we put an m in front of the \(\angle\) sign to indicate measure. So, \(m \angle XUY = 84^\) , \(m \angle YUZ = 42^\) and \(m \angle XUZ = 126^\) .

    What is the measure of the angle shown below?

    Solution

    This angle is not lined up with 0∘, so use subtraction to find its measure. It does not matter which scale you use, as long as you are consistent.

    Use a protractor to measure \(\angle RST\) below.

    Solution

    Lining up one side with \(0 ^\) on the protractor, the other side hits \(100 ^\) .

    What is \(m \angle QRT\) in the diagram below?

    Solution

    Using the Angle Addition Postulate, \(m\angle QRT = 15^+30^=45^\) .

    Review

    1. What is \(m \angle LMN\) if \(m \angle LMO = 85^\) and \(m \angle NMO = 53^\) ?

    2. If \(m \angle ABD = 100^\) , find \(x\) .

    For questions 3-6, determine if the statement is true or false.

    1. For an angle \(\angle ABC\) , \(C\) is the vertex.
    2. For an angle \(\angle ABC\) , \(\overline\) and \(\overline\) are the sides.
    3. The \(m\) in front of \(m \angle ABC\) means measure.
    4. The Angle Addition Postulate says that an angle is equal to the sum of the smaller angles around it.

    For 7-12, draw the angle with the given degree, using a protractor and a ruler.

    For 13-16, use a protractor to determine the measure of each angle.

    1. Figure \(\PageIndex\)
    2. Figure \(\PageIndex\)
    3. Figure \(\PageIndex\)
    4. Figure \(\PageIndex\)

    Review (Answers)

    To see the Review answers, open this PDF file and look for section 1.5.

    Vocabulary

    TermDefinition
    AngleA geometric figure formed by two rays that connect at a single point or vertex.
    ProtractorA protractor is a tool used to measure an angle in terms of degrees.
    VertexA vertex is a point of intersection of the lines or rays that form an angle.

    Additional Resource

    Video: Angle Basics

    Activities: Angle Measurement Discussion Questions

    Study Aids: Angles Study Guide

    Practice: Measuring Angles

    Real World: Angle Measurement

    Recommended articles

    1. Article type Section or Page License CK-12 Show Page TOC No on Page
    2. Tags
      1. authorname:ck12
      2. program:ck12
      3. source@https://www.ck12.org/c/geometry
      4. source[translate]-k12-2136