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
1.0x

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 Content
  1. Constructing a Regular Pentagon from a Square

    Slide 1 - Constructing a Regular Pentagon from a Square

    • You need to know the basic compass and straightedge constructions!!!
    • BEGIN
  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.

    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. 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.

    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. Now use your compass to draw a circle with center M and passing through point C.

    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. D

    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. Now draw a circle with center C that passes through B.

    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. The last two circles drawn intersect twice. We will use the rightmost of those two points, and connect it to point C

    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. This will now give us  a second side of our pentagon.

    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. Now we repeat this construction with E as a vertex.

    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. Now we repeat this construction with E as a vertex.

    Slide 10 - Now we repeat this construction with E as a vertex.

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

    Slide 11 - D

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