# Constructing a Regular Pentagon from a Square

## Using Euclidean construction tools (compass and straightedge), you ca create a regular pentagon from a square.

Geometry construction pentagon

# Constructing a Regular Pentagon from a Square

Created 3 years ago

Duration 0:00:00
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Using Euclidean construction tools (compass and straightedge), you ca create a regular pentagon from a square.
Slide Content
1. ### Slide 1 - Constructing a Regular Pentagon from a Square

• You need to know the basic compass and straightedge constructions!!!
• BEGIN
2. ### 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
3. ### 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
4. ### 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
5. ### 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
6. ### 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
7. ### 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
8. ### 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
9. ### 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
10. ### Slide 10 - Now we repeat this construction with E as a vertex.

• Then again with F as a vertex
• D
• Click to continue
11. ### Slide 11 - D

• Now we got it!!!
• We have made a regular pentagon, starting with a square!!