4. CONDITIONS FOR REGULAR POLYGON
• Two conditions
• 1. every side must of the same length (equilateral)
• AND
• 2. every internal angle must of the same angle.
(equiangular)
Note we need both conditions to make a polygon to
be regular. Only one condition is NOT enough to
make a polygon to be a regular polygon. In the next
few slides, I am going to show why we need both
conditions
5. EQUIANGULAR
Pentagon ABCDE is a
regular polygon
Lines ED and FG are
parallel
The internal angles E and F
are the same (corresponding
angles of parallel line)
For the same reason, angle
G and D are the same.
Therefore, we just created
an equiangular pentagon but
not a regular pentagon
6. • We have just learnt that equiangular is not a
sufficient condition for a polygon being regular.
• How about equilateral? Should a equilateral polygon
be regular polygon?
• The answer is NO. I will explain it in the next slide
7. REGULAR PENTAGON
The red polygon is a regular polygon
All internal angles and sides are the
same
The circles are to show the
pentagon’s sides are of the same
length (equilateral)
8. IRREGULAR EQUILATERAL PENTAGONS
The blue pentagons above are equilateral but not regular. The red
regular pentagons are there to compare with the irregular ones.
9. CONCLUSIONS
• To make a polygon to be regular, it must be
• 1. Equiangular
• 2. Equilateral
