what are the steps for using a compass and straightedge to construct the bisector of ∠a?

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You tin can bisect an angle just every bit you can bisect a line. To bisect means to divide something into two equal parts. There are two methods for bisecting an bending. You can use the first method if yous accept a protractor, and if yous need to find the caste measurement of the bisector. You tin use the second method if yous have a compass and straightedge, and only need to draw the bisector, not measure it.

1. 1

   Measure the angle. Place the origin hole of the compass on the angle's vertex, lining upwardly the base of operations line with one of the angle's rays. Look at the degree marker where the other ray falls. This will tell you the degree measurement of the bending.

   • For case, you lot might mensurate an angle that is 160 degrees wide.
   • Remember that protractors have two sets of numbers. To know which set of numbers to look at, think near the size of the angle. Obtuse angles are greater than 90 degrees, and acute angles are less than 90 degrees.

2. two

   Split up the number of degrees in one-half. An angle bisector divides an angle into two equal parts.^[i] So, to notice where the bending bisector lays, divide the number of degrees in the angle past 2.^[2]

   • For instance, if the angle is 160 degrees, y'all would calculate ${\displaystyle {\frac {160}{2}}=80}$ . So, the angle bisector is at the 80-degree mark of the angle.

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3. 3

   Draw a point marking the measurement of the bisector. Once again, line up the origin hole with the angle's vertex, and line upwards the base line with one of the rays. Detect the halfway point using the protractor. Marker this point in the bending'southward interior.

   • For case, if the bisector of a 160-caste angle lies at the lxxx-degree signal, you would discover the 80-degree mark on the protractor and describe a indicate at this location in the angle'southward interior.

4. four

   Draw a line from the vertex to the point. Use the straightedge of the protractor to connect the vertex to the halfway signal of the bending. The line you depict is the bending'south bisector.^[iii]

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1. 1

   Describe an arc across both rays. Open the compass to whatsoever width, and place the point of the compass at the angle's vertex. Swing the compass so that the pencil draws an arc that crosses both rays of the angle.^[4]

   • For example, you lot might have bending BAC. Place the compass tip on indicate A. Swing the compass so that information technology draws an arc intersecting ray AB at point D, and ray Ac at point Eastward.

2. 2

   Draw an interior arc. Move the compass then that the point sits on the location where the first arc intersects the first ray. Swing the compass, drawing an arc inside of the angle.^[5]

   • For example, place the compass tip on point D and describe an arc inside the bending.

3. 3

   Draw a second interior arc intersecting the start interior arc. Without irresolute the width of the compass, motility the point to the location where the commencement arc intersects the second ray. Swing the compass, drawing an interior arc that intersects the offset interior arc you drew.^[vi]

   • For instance, place the compass tip on signal E and describe an arc intersecting the first interior arc. Label the point of their intersection point F.

4. iv

   Draw a line from the vertex to the point where the arcs intersect. Use a straightedge to ensure that the line is authentic. This line bisects the angle.^[7]

   • For example, utilise a straightedge to draw a line connecting points F and A.

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Add New Question

• Question

  What is the number of bisectors that can be fatigued of a given bending?

  

  One.

• Question

  How do I prove that the ray fatigued bisects the angle?

  

  Bank check the angles betwixt either of the original rays and the bisector line. If they are equal, then the line is the verbal bisector.

• Question

  How can I draw more than i angle bisector?

  

  Any given bending has exactly ane bisector.

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Article Summary X

An angle bisector divides an angle into 2 equal parts. The easiest way to construct a bisector of a given bending is with a protractor. Showtime, measure the bending by placing the origin hole of the protractor on the angle'southward vertex and lining upwards the baseline with 1 of the bending's rays. Take the angle you go and dissever this number by 2. For example, if the angle is 160 degrees, you would divide this by 2 to get fourscore. The bisector of this bending is fourscore degrees. Once you lot take this number, line upwardly your protractor with the bending again, and mark the halfway point. For example, if the bisector of a 160-degree angle lies at the eighty-degree point, y'all would find the 80-degree marker on the protractor and depict a betoken at this location in the angle'south interior. To construct your bisector, simply draw a line from the vertex of the angle to the point you lot just drew. To learn how to construct a bisector with a compass, read on!

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