In geometry it is possible to draw the bisector of an angle, a segment, a triangle or a polygon in general. The bisector of an angle is the straight line which, starting from the vertex, divides it into two congruent parts. There are two ways to draw the bisector of an angle. In the first case you can use a normal protractor to also measure the width of the two new angles created by the bisector; in the second case you can use a compass and a ruler, but without the protractor you will not be able to measure the width of the two new angles created by the bisector.
Steps
Method 1 of 2: Using a Protractor
Step 1. Measure the starting angle
Place the pointer of the protractor on the origin (or vertex) of the angle. Align the underside of the tool (the base) with either side of the corner. Now look at the point on the protractor scale indicated on the other side of the corner. The number you will read represents the width of the angle you are studying.
- For example, let's assume that the amplitude of the angle measured with the protractor is 160 °.
- Remember that the protractor has two measurement scales. To find out which numbering to refer to, you will need to look at the structure of the corner under consideration. The "obtuse" angles have an amplitude greater than 90 °, while the acute angles have an amplitude less than 90 °.
Step 2. Divide the resulting number by two
The bisector of an angle divides it into two equal parts, so to be able to draw the bisector of an angle you will need to divide its relative amplitude in degrees in half.
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Continuing with the previous example relating to an angle of 160 ° you will get 1602 = 80 { displaystyle { frac {160} {2}} = 80}
. La bisettrice dell'angolo in oggetto verrà quindi tracciata con un'angolazione di 80°.
Step 3. Draw a small mark where the angle bisector will pass
Place the pointer of the protractor again on the vertex (or origin) of the starting angle and align the base of the tool with one of the two sides of the angle. Find the point that is half the original angle width.
In the example above, the bisector of a 160 ° angle passes exactly 80 °, so you will need to draw a small dot at this angle of the protractor. Remember to draw it inside the original corner
Step 4. Now draw a line starting from the vertex of the corner and passing through the point you drew in the previous step
Use a ruler or the base of the protractor to draw a straight line joining the vertex of the starting angle and the point you just drew. The line you get will be the bisector of the angle.
Method 2 of 2: Using a Compass
Step 1. Draw an arc that intersects both sides of the corner
Open the compass at any angle, place the needle on the vertex of the corner, then draw two small arcs at the point of intersection with the sides of the corner under consideration.
For example, assume you have the BAC angle. Place the compass needle at point A; at this point draw a small arc that intersects side AB at point D and side AC at point E
Step 2. Now draw an arc inside the corner
Move the compass so that the needle is positioned exactly where the arc you drew in the previous step intersects either side of the corner. Now rotate the compass to draw an arc inside the corner.
Continuing with the previous example, place the compass needle on point D and draw an arc inside the corner
Step 3. Draw a second arc that intersects the one drawn in the previous step
Without changing the width of the compass, position the needle at the intersection point of the second side of the corner with the starting arc. Now draw a second arc inside the corner, so that it intersects the one you drew in the previous step.
Continuing with the previous example, place the compass needle at point E and draw a second arc inside the corner that intersects the one already present. The point of intersection of the two arcs will be point F
Step 4. Draw a line starting from the vertex of the corner and passing through the intersection point F of the two arcs present inside the corner
Use a ruler to be as accurate as possible. The resulting line will be the bisector of the starting angle.
