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A is a five-sided polygon that is formed by connecting five line segments. Each line segment is equal in length, and each angle measures 108 degrees. The pentagon is a popular shape in architecture, art and science. In this article, we will discuss how to construct a regular pentagon given the side length.

Method 1: Using a Compass and Straightedge

To construct a regular pentagon, you will need a compass and a straightedge. The steps involved in constructing a pentagon with a compass and straightedge are as follows:

Step 1: Draw a straight line segment of the desired length, which will represent one side of the pentagon.

Step 2: Set your compass to the length of the line segment. Place the point of the compass on one end of the line segment and draw an arc. Do the same on the other end of the line segment.

Step 3: Without changing the size of your compass, place the point of the compass on the intersection of the two arcs and draw another arc above the line segment.

Step 4: Place the point of the compass on the intersection of the second arc and the line segment. Draw an arc that intersects the second arc.

Step 5: Place the point of the compass on the new intersection and draw another arc that intersects the first arc.

Step 6: Connect the points of intersection with straight . This will form a regular pentagon.

Method 2: Using a Protractor

To construct a pentagon using a protractor, you will need a protractor, a ruler and paper. The steps involved in constructing a pentagon using a protractor are as follows:

Step 1: Draw a straight line segment of the desired length.

Step 2: Use a protractor to measure a 108-degree angle at one end of the line segment. Mark the endpoint of the angle.

Step 3: Use the protractor to measure another 108-degree angle at the endpoint of the first angle. Mark the endpoint of the second angle.

Step 4: Use the protractor to measure another 108-degree angle at the endpoint of the second angle. Mark the endpoint of the third angle.

Step 5: Continue measuring and marking 108-degree angles until you have five points. These points will form a pentagon.

Step 6: Connect the points with straight lines to form a regular pentagon.

In conclusion, constructing a pentagon with equal sides can be challenging. However, using these two methods, specifically using a compass and straightedge or a protractor, can help you construct a pentagon with ease. These methods do not require any special skills or tools, and all you need is a little bit of patience and time. So, go ahead and start constructing your perfect pentagon today!

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