Constructing a regular pentagon, a five-sided polygon with equal length sides, might seem challenging at first glance. However, with the right tools and techniques, you can easily create a perfect pentagon based on the length of just one side. In this guide, we’ll walk you through the step-by-step process to construct a pentagon with precision.

Materials Needed

  • Compass
  • Straightedge
  • Pencil
  • Protractor

Step 1: Draw the Baseline

Start by drawing a horizontal line segment of the desired length, which will serve as the baseline for your pentagon. Ensure it is straight and accurately measures the length you want for each side of your pentagon.

Step 2: Construct Equilateral Triangle

Using the endpoint of the baseline as the center, open your compass to the length of the baseline, and draw a circle that intersects the baseline at two points. This circle will be the arc for the first side of the pentagon.

Keeping the compass at the same width, place your compass point on one of the intersection points on the baseline. Draw an arc that intersects the first arc you drew. Repeat this step from the other intersection point. These arcs will create an equilateral triangle.

Step 3: Complete the Pentagon

Looking at the newly constructed equilateral triangle, find the point where two sides of the triangle intersect. Place the compass point on this intersection point and adjust the compass width to reach one of the triangle’s vertices.

With the compass set, draw an arc starting from the vertex of the equilateral triangle and intersecting one of the baseline’s endpoints. Repeat this step from the other vertex to create the remaining two sides of the pentagon.

Next, using your straightedge, draw lines connecting the endpoints of the baseline to the endpoints of the newly created pentagon sides. This outlines the complete pentagon shape.

Step 4: Check for Accuracy

Ensure the pentagon is accurately constructed by measuring each side with a ruler or protractor. If any side differs slightly from the desired length, make the necessary adjustments.

Constructing a pentagon given the length of one side may appear complex, but with the correct steps, you can easily create this five-sided polygon. By following this guide and paying attention to accuracy, you can now confidently construct a perfect pentagon based on a single side length. Happy constructing!

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