Is the interior of an angle a convex set?

[LCharette]

I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.

 

[Office_Shredder]

I need to prove the interior of <ABC is a convex set. I know it is. I started by defining the angle as the intersection of two half planes and using the fact that each half plane is convex. I am stuck on where to go from here.

If you could prove the intersection of two convex sets is convex as well you'd be set

 

[LCharette]

Do you have any suggestions on how to prove the intersection of two half planes is convex?

 

[HallsofIvy]

Let p and q be in the intersection of convex sets A and B.

p and q are both in A so ...

p and q are both in B so ...