Download Construct a Regular Hexagon - Math in Mind

Name ______________________________
Class Geometry
Date _________________
Class Period _________________
Construct a Regular Hexagon
Be sure to leave your construction marks visible!
Regular Hexagon with Given Length
AB
Given:
Construct: hexagon CDEFGH such that
CD = DE = EF = FG = GH = HC = AB
∠C≅ ∠D≅ ∠E≅ ∠F≅ ∠G≅ ∠H
a line segment
hexagon
all sides equal to given length
all angles congruent
A
B
Step 1.
Open the compass to the distance between points A and B. Keep the compass at
this setting for the entire construction.
Step 2.
Mark a point to use as the center of a circle somewhere in the middle of your
construction space. Place the point of the compass on this point and draw a circle.
Step 3.
Mark any point on the circumference of the circle. Label this point C. It will be the
first vertex of the hexagon.
Step 4.
Put the point of the compass on point C and draw an arc until it crosses the
circumference of the circle you drew in step 2. The intersection point where the arc
crosses the circle is another vertex of the hexagon. Label that point as point D.
Step 5.
Put the point of the compass on point D and mark another arc on the circle. That
intersection point is point E.
Step 6.
Keep going around the circle, marking points F, G, and H with the same technique.
At point H, the next arc drawn should cross the circle at point C. This confirms that
the construction is well done.
Step 7.
Use a straightedge to draw line segments between consecutive points to create the
hexagon.