Regular Polygons

1
Regular Polygons

• In Round Robin Tournaments

2
Definitions

• Polygon a closed plane figure, having three
  or more, usually straight, sides.
• Regular Polygons polygon whose sides
  are the same length and angles are same measure

3
Theorem

• Regular Polygon Symmetry Theorem
• n-sided figure will have n lines of symmetry
• Perpendicular bisectors of each segment
• Angle bisectors of each angle

4
ANGLES AND SIDES ARE EQUAL
Means congruent sides
or
or
Means congruent angles
5
Regular Pentagon
5 sides 5 lines of symmetry
6
Regular Hexagon
ETC.
6 SIDES 6 LINES OF SYMMETRY
7
Round Robin Tournaments

• Can be shown using regular polygons
• Bye when a team is not playing another team
• Chord segment connecting two points on a circle

8
5 team R.R.T
360 / 5 72
A

• Start with a circle
• Divide 360º by the number of teams
• Use a protractor to measure every 72 degrees of
  the circle
• Letter each point
• Connect points A and B and parallel points
• Continue Counterclockwise

E
B
D
C
9
Inscribed---

• InscribeLaying inside a figure
• What was inscribed in the circle?

!!A PENTAGON!!
5 SIDES AND 5 TEAMS
10
In words

• Round 1 AB EC Bye D
• Round 2 AE BD Bye C
• Round 3 ED AC Bye B
• Round 4 DC EB Bye A
• Round 5 CB DA Bye E

Teams that have no other team to play during a
round.
11
6 Team Round Robin
Dont Assume That You Use the Same Steps!
12
6 team
B
C

• Again start with a circle
• This time divide 360º by 5 again instead of 6
• Use protractor to measure degrees
• Label and put F in middle
• Connect A and B, same as in a 5 team. Then
  connect parallel and remaining teams
• Continue Counterclockwise

A
F
360/5 72
D
E
13
Not as easy to interpret as 5 team
14
In words

• Round 1 AB EC DF Bye Ø
• Round 2 BC DA EF Bye Ø
• Round 3 CD BE AF Bye Ø
• Round 4 DE AC BF Bye Ø
• Round 5 EA DB CF Bye Ø

Even number of teams means no byes!
15
Should be Able to Figure Out

• How many rounds?
• How many byes?
• How many games?
• What is the inscribed figure?