Constructing a Regular Pentagon from a Square
Created 3 years ago
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Using Euclidean construction tools (compass and straightedge), you ca create a regular pentagon from a square.

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Slide 1  Constructing a Regular Pentagon from a Square
 You need to know the basic compass and straightedge constructions!!!
 BEGIN

Slide 2  The first step is to use the perpendicular bisector of a segment construction to locate the midpoint of a side. We will use side AB here.
 The right side of the square will be the first side of our regular pentagon.
 Click to continue

Slide 3  The first step is to use the perpendicular bisector of a segment construction to locate the midpoint of a side. We will use side AB here.
 Let’s call the midpoint M.
 Now use your compass to draw a circle with center M and passing through point C.
 Click to continue
 Click to continue

Slide 4  Now use your compass to draw a circle with center M and passing through point C.
 Use your straightedge to extend side AB to the right out to the circle.
 Click to continue
 Click to continue

Slide 5  D
 Now open up your compass to the distance from point G to point D
 Use this distance as the radius, and draw a circle using B as center.
 Click to continue
 Use your straightedge to extend side AB to the right out to the circle.
 Click to continue

Slide 6  Now draw a circle with center C that passes through B.
 D
 Click to continue
 Use this distance as the radius, and draw a circle using B as center.
 Click to continue

Slide 7  The last two circles drawn intersect twice. We will use the rightmost of those two points, and connect it to point C
 D
 Use this distance as the radius, and draw a circle using B as center.
 Click to continue
 Click to continue

Slide 8  This will now give us a second side of our pentagon.
 Now we must do our construction for copying an angle. We will copy angle BCD with CD as a side and D as the vertex.
 D
 The last two circles drawn intersect twice. We will use the rightmost of those two points, and connect it to point C
 Click to continue
 Click to continue

Slide 9  Now we repeat this construction with E as a vertex.
 D
 Now we must do our construction for copying an angle. We will copy angle BCD with CD as a side and D as the vertex.
 Click to continue
 Click to continue

Slide 10  Now we repeat this construction with E as a vertex.
 Then again with F as a vertex
 D
 Click to continue

Slide 11  D
 Now we got it!!!
 We have made a regular pentagon, starting with a square!!