Which step is the same when constructing an inscribed square and an inscribed regular hexagon?
2 answers:
Answer:
Construct a circle first
Step-by-step explanation:
If you're going to inscribe any figure in a circle, the first construction you need to do is <em>construct the circle</em>.
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<em>Additional comment</em>
The attached shows our construction of an inscribed square and an inscribed regular hexagon. Here are the steps we used. You will notice the first step is <em>construct a circle</em>. (It could be, <em>construct line AB</em>, then construct circle A with radius AB.)
We have used line AB in the construction of the hexagon, but the hexagon could have been constructed without it. That is why "construct a circle first" is likely a better choice for a common first step.
<u>square</u>
- construct circle A and locate a point B on it
- construct line AB, and locate point C at the other intersection of AB and circle A
- set the compass to greater than half the diameter
- using B as a center, draw arc RS
- using C as a center, draw arc RS using the same compass setting. Label the intersection points R and S.
- draw line RS. Label the points of intersection with the circle as T and U.
- draw inscribed square CTBU
<u>regular hexagon</u>
- construct circle A and locate a point B on it
- construct line AB, and locate point C at the other intersection of AB and circle A
- without changing the compass, using B as a center, draw arc KL. Label intersection points K and L.
- using C as a center, draw arc JM. Label intersection points J and M.
- draw inscribed hexagon CJKBLM
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Arguably, the first step to constructing a circle is <em>set the compass to the radius</em>. We chose to ignore this because one of the ways to construct an inscribed hexagon is to mark off successive arcs around a circle that have a radius equal to the radius of the circle. We did not use that method. (The use of diameter BC made drawing 5 arcs around the circle unnecessary. We drew 2 instead.)
Or, you could argue that <em>construct a line first</em> is needed before you set the compass to the radius. If this is the first step, then the next steps would be to <em>mark the center of the circle</em> on the line, and <em>mark another point at a distance of the radius</em> from that center point.
What you consider to be the first step depends on the level of detail you want to attend to.
After the construction of a circle, we have to "Set the compass to the radius of the circle" so, option C is correct.
<h3>What is a regular hexagon?</h3>A regular hexagon is defined as a closed shape consisting of six equal sides and six equal angles. The sum of the measure of angles of a regular hexagon is 120 degrees.
Steps to create an inscribed hexagon:
1: The structure needs to adjust the box thickness towards that radius.
2: Afterward moves around the outside of the circular path to just produce the 6 vertices of that similar hexagon.
"Set the compass to the radius of the circle" so, option C is correct.
Thus the above answer is correct.
Learn more about inscribed hexagons here:
#SPJ1
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