How to Construct a Bisector of a Given Angle: 8 Steps

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How to Construct a Bisector of a Given Angle: 8 Steps
How to Construct a Bisector of a Given Angle: 8 Steps
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You can split an angle the same way you split a line. In this case, it is said that the bisector of an angle was constructed, dividing it into two equal parts. There are two methods for this. First, a protractor can be used to find the measurement in degrees of the desired angle. The second method, however, makes use of a compass and a ruler, being only necessary to draw the bisector instead of measuring it.

Steps

Method 1 of 2: Constructing the Bisector with a Protractor

Construct a Bisector of a Given Angle Step 1

Step 1. Measure the angle

Place the origin point of the protractor at the vertex, aligning it with the baseline on one of its sides. Note the degree mark where the other side meets. Doing so will indicate which angle measure is being studied.

  • Example:

    suppose you have found an angle of 160{displaystyle 160}

    °.

  • Lembre-se de que transferidores têm dois conjuntos de números. Para saber qual deles deve ser usado, pense no tamanho do ângulo. Os obtusos são maiores que 90{displaystyle 90}
  • °, enquanto os agudos são menores que 90{displaystyle 90}

    °.

Construct a Bisector of a Given Angle Step 2

Step 2. Divide the number in degrees in half

The bisector divides the angle into two equal parts. So, to find out where it is, just divide the measure of the angle in question by 2{displaystyle 2}

  • Exemplo:

    se o ângulo for de 160{displaystyle 160}

    °, você calculará 1602=80{displaystyle {frac {160}{2}}=80}

    , de modo que a bissetriz se encontra na marca de 80{displaystyle 80}

    °.

Construct a Bisector of a Given Angle Step 3

Step 3. Make a point marking the measurement of the bisector

Re-align the protractor's origin point with the vertex, and the baseline with one of its sides. Find the halfway point with the protractor and mark it inside the angle.

  • Example:

    if the angle bisector of 160{displaystyle 160}

    ° se encontra aos 80{displaystyle 80}

    °, você encontrará esse valor no transferidor e, a seguir, fará ali um ponto no interior do ângulo.

Construct a Bisector of a Given Angle Step 4

Step 4. Draw a line from vertex to point

Use the protractor ruler to connect the apex to the middle point. The line drawn will, in turn, be the bisector of the angle.

Method 2 of 2: Constructing the Bisector with a Compass

Construct a Bisector of a Given Angle Step 5

Step 1. Draw an arc crossing both sides

Open the compass any distance and place its point at the vertex. Make it a semicircle that goes through both sides of the angle.

  • Example:

    you are working with angle BA^C{displaystyle B{hat {A}}C}

    . Coloque a ponta do compasso em A^{displaystyle {hat {A}}}

    e use-o para desenhar um arco que cruze AB{displaystyle AB}

    no ponto D{displaystyle D}

    e AC{displaystyle AC}

    no ponto E{displaystyle E}

Construct a Bisector of a Given Angle Step 6

Step 2. Draw an inner semicircle

Move the compass so that the point rests where the first arc and the first side intersect. Use the compass to draw this semicircle within the angle area.

  • Example:

    place the compass end at point D{displaystyle D}

    e desenhe um arco dentro do ângulo.

Construct a Bisector of a Given Angle Step 7

Step 3. Draw a second inner semicircle that intersects with the first

Without changing the gauge of the compass, bring the point where the first bow intersects with the second side. Use the compass to draw this inner semicircle across the first one.

  • Example:

    place the compass end at point E{displaystyle E}

    e desenhe um arco cruzando o primeiro semicírculo interno, denominando o ponto de intersecção F{displaystyle F}

Construct a Bisector of a Given Angle Step 8

Step 4. Draw a line from the vertex to the crossing point of the arcs

Use a ruler to make it completely straight, dividing the angle into two equal parts.

  • Example:

    use a ruler to draw a line joining the points F{displaystyle F}

    e a{displaystyle a}

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