Prove the Int<ABC is a convex set.

[LCharette]

Homework Statement

Prove the Int<ABC is a convex set.

Homework Equations

The Attempt at a Solution

1. Int <ABC = H(A,BC) intersect H(C,AB) by the definition of interior.
2. H(A,BC) is convex and H(C,AB) is convex by Half-Plane Axioms

I know I need to show the intersection of the two half planes is convex but I do not know how to do this.

 

[HallsofIvy]

It would help if you would tell us what "ABC" is! Are "A", "B", "C" points and "ABC" the region bounded by the triangle with those vertices?

 

[Office_Shredder]

Regardless of the notation, once you get to

I know I need to show the intersection of the two half planes is convex but I do not know how to do this.

Prove in general that the intersection of two convex sets is convex