Proofing A Geometric Statement

[Bashyboy]

I've attached a picture that pertains to the query that I have. I have been able to show that each angle B is 60 degrees, but I am unsure as to how to show a is also a 60 degree angle. Isn't there some geometric theorem I could use?

 

[Enigman]

Well, the sum of angles in a triangle.

 

[Bashyboy]

Well, I am first trying to prove that each object in the hexagon is a triangle. So, I can't use that fact.

 

[SteamKing]

If the figure is closed and it's got three sides, it's a triangle. There's your proof.

 

[Bashyboy]

All right, so I know that each angle is equivalent to each other, when you consider one single triangle. Is this sufficient to show that it must be a equilateral triangle, or must I also so that each side has the same length?

 

[SteamKing]

If you know that two interior angles of a triangle are both 60 degrees, then you can determine the third angle.

If all interior angles are the same, IPSO FATSO, it's an equilateral triangle.

 

[Ray Vickson]

All right, so I know that each angle is equivalent to each other, when you consider one single triangle. Is this sufficient to show that it must be a equilateral triangle, or must I also so that each side has the same length?

What material have you studied so far? All the properties you need are standard, elementary geometry (but, unfortunately, sometimes that is not taught any more).