Prove polygon w/ n sides has n vertices; w/ n vertices has n sides

[shahar]

(1) How can I prove that polygon with n sides has n vertexes?
(2) How can I prove that polygon with n vertexes has n sizes?

 

[lev888]

(1) How can I prove that polygon with n sides has n vertexes?
(2) How can I prove that polygon with n vertexes has n sizes?

Try induction.

 

[Dr.Peterson]

(1) How can I prove that polygon with n sides has n vertexes?
(2) How can I prove that polygon with n vertexes has n sizes?

The details may depend on what definition you are using. How are you defining "polygon"?

 

[shahar]

Definition?!

The details may depend on what definition you are using. How are you defining "polygon"?

I know that polygon is broken line that close.

What other definitions can be of the word "polygon"?

 

[Deleted member 4993]

I know that polygon is broken line that close. ...... Intersecting or non-intersecting

What other definitions can be of the word "polygon"?

.

 

[Dr.Peterson]

I know that polygon is broken line that close.

What other definitions can be of the word "polygon"?

I asked because if you were told to write a proof, you need a specific definition on which to base the proof. With only an informal "definition", it's harder to be sure what steps are legal. Are you required to write a formal proof?

Informally, you might just consider tracing your "broken line" in one direction, and match up each edge with the vertex at its start. That gives you a one-to-one correspondence between the two sets.

 

[HallsofIvy]

Each edge has two vertices, each vertex connects two edges. Does that give you a one-to-one correspondence.