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Question
How to draw regular pentagon & hexagon symmetry?
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Solution
The following is the procedure that is used to construct a regular pentagon:
Step 1
Draw a circle with a centre O.
Step 2
Randomly choose a point on the circle and name it A. This point will become one of the vertices of the Pentagon. Draw a line that passes through point A and the centre O.
Step 3
Construct a line which is perpendicular to line OA and passing through the centre of the circle, O. Name one of the sides that the line intersects with the circle as B
Step 4
Establish the midpoint of line OB, name it as point C and draw a circle centred at C and passes through point A as shown: Mark the point where the circle intersects with line OB inside the original circle as the point D.
Step 5
Draw a circle with its centre at point A and passes through point D. Mark the points where the circle intersects with the original circle as points E and F.
Step 6
Draw another circle with its centre at point E and passes through point A. Name the point where the circle intersect with the original circle as G
Step 7
Draw the last circle which has its centre at point F and passes through point A. Name the point where it intersects with the original circle as point H.
Step 8
Now construct a regular pentagon AEGHF The polygon marked with a maroon line represents a regular pentagon with points A, E, G, H and F as its vertices.
The process of constructing a pentagon is a heck of a process but it is quite easy to master. Once you’ve constructed the first circle which intersects with the initial circle that was constructed, then you will have your work half done.
In order to master the whole process, you will, of course, need to go through it twice or three times while practising it in order to have a real grasp of it.
Remember that every interior angle of a pentagon measures 108˚ and you can be able to verify this if your construction was right.
Construction of a Regular Hexagon
Let us now look at the construction of a regular hexagon using a ruler and a compass. As we had said before, a regular hexagon has a perfect symmetry and thus is one of the easiest polygons to construct. The following is the procedure used to construct a regular hexagon using a ruler and a compass:
Step 1
Construct a circle with a centre O and draw its diameter.
Step 2
Without changing the width of the compass, place its point on each of the points where the diameter intersects with the circle and make arcs as shown
Step 3
Now join all the points where the arcs and the diameter intersect with the circle as shown:
The maroon line in the figure represents a regular hexagon. If your drawing was accurate enough, you will realise that all the sides are equal in length and also all the interior angles are equal in measure.
Step 1
Draw a circle with a centre O.
Step 2
Randomly choose a point on the circle and name it A. This point will become one of the vertices of the Pentagon. Draw a line that passes through point A and the centre O.
Step 3
Construct a line which is perpendicular to line OA and passing through the centre of the circle, O. Name one of the sides that the line intersects with the circle as B
Step 4
Establish the midpoint of line OB, name it as point C and draw a circle centred at C and passes through point A as shown: Mark the point where the circle intersects with line OB inside the original circle as the point D.
Step 5
Draw a circle with its centre at point A and passes through point D. Mark the points where the circle intersects with the original circle as points E and F.
Step 6
Draw another circle with its centre at point E and passes through point A. Name the point where the circle intersect with the original circle as G
Step 7
Draw the last circle which has its centre at point F and passes through point A. Name the point where it intersects with the original circle as point H.
Step 8
Now construct a regular pentagon AEGHF The polygon marked with a maroon line represents a regular pentagon with points A, E, G, H and F as its vertices.
The process of constructing a pentagon is a heck of a process but it is quite easy to master. Once you’ve constructed the first circle which intersects with the initial circle that was constructed, then you will have your work half done.
In order to master the whole process, you will, of course, need to go through it twice or three times while practising it in order to have a real grasp of it.
Remember that every interior angle of a pentagon measures 108˚ and you can be able to verify this if your construction was right.
Construction of a Regular Hexagon
Let us now look at the construction of a regular hexagon using a ruler and a compass. As we had said before, a regular hexagon has a perfect symmetry and thus is one of the easiest polygons to construct. The following is the procedure used to construct a regular hexagon using a ruler and a compass:
Step 1
Construct a circle with a centre O and draw its diameter.
Step 2
Without changing the width of the compass, place its point on each of the points where the diameter intersects with the circle and make arcs as shown
Step 3
Now join all the points where the arcs and the diameter intersect with the circle as shown:
The maroon line in the figure represents a regular hexagon. If your drawing was accurate enough, you will realise that all the sides are equal in length and also all the interior angles are equal in measure.
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