Regular Pentagons

Question

Prove that the diaganols inside a regular pentagon forms another regular pentagon

Answer 1

A quick proof goes something like this.

It;s not a rigorous proof, but a general strategy

and outline of a formal proof. You can investigate

and provide the details of each step.

 

The diagonals create 5 congruent isoceles triangles.

 

Now, if the smaller pentagon on the inside is removed,

the 5 pointy tips of the star remain, forming 5 smaller

triangles.

 

By CPCTC of the isoceles triangles, those 5 smaller

triangles are congruent by SAS. That is , the 5 pointy

tips of the star are congruent.

 

Since the base of those 5 smaller triangles form the 

interior pentagon and those bases are all congruent

by CPCTC of the "pointy tips" smaller triangles,

the interior pentagon is regular.