6th Grade Math Textbook, Progress

Construct a Regular Polygon

You can construct a regular polygon by using a circle.

To construct a regular hexagon, follow these steps.

Construct each regular polygon by using a circle. Explain your process.

20. an equilateral triangle 21.a square 22. a regular dodecagon

A regular polygon has

congruent sides and

congruent angles.

Step 1

Use a compass to

construct a circle. Put

the compass point

anywhere on the circle.

With the same radius

as the circle, construct

an arc that intersects

the circle at point A.

Step 3

Repeat Step 2 all the way

around the circle. Label

the points of intersection

C, D, E, and F. With a

straightedge, draw the

segments joining the

points. ABCDEFis a

regular hexagon.

For each statement, write always, sometimes, ornever.

10. All radii of a circle have the same length.


11. Chords are diameters.


12. A central angle has its vertex on
    the circle.

Use a compass to construct a circle. Then do the following:

16. Draw and label the diameter A
    B
    .


17. Draw the chords A
    C
    and B
    C
    .
    24. Circle Xhas two intersecting diameters, A
    
    B
    and C
    D
    . If m
    AXC
    75°, what are the
    measures of the other three central angles?


18. Draw any point C on the circle.


19. Name the figure you have drawn.


20. Some arcs are line segments.


21. All circles are regular polygons.


22. The longest chord of any circle
    is its diameter.


23. Alex draws circle Owith a diameter
    of 12 inches. What is the length of a
    radius of the circle O?

Step 2

With the same radius

as the circle, put the

compass point at Aand

construct another arc

that intersects the circle

at point B.

A A

B

A

D C

E

F

B

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