Constructing a Pentagon

1
Constructing a Pentagon

• Emelie Day
• Lesson 41

2
What do you know

• 1 2 3 4
• 5 6 7 8

3
Answers

• Numbers 4, 5, and 8 are regular polygons
• Numbers 1, 2, 3, 6, and 7 are not
• To tell you need to look at lengths and angles

4
Decagon with radius 1
5
Closer Look

• What is the measure of angle AOB, OAB, and OAC?
• What is the proportion to find x?
• What are triangles OAC and ACB? Similar or
  congruent?

O
1
x
C
x
1-x
A
B
x
6

• What is the measure of angle AOB, OAB, and OAC?
• AOB 36
• OAB 72
• OAC 36
• What is the proportion to find x?
• 1/xx/(1-x)
• What are triangles OAC and ACB? Similar or
  congruent?
• Similar triangles

O
1
x
C
x
1-x
A
B
x
7
Closer Look (Cont)

• 1/xx/(1-x)
• X2x-10
• X (radical 5-1)/2