So look at the first one like this: AB=BC which means its an isosceles triangle(search that for more details) and automatically has the 2 angles of equal measures.
The second one the same thing but reversed.(angles first)Sides opposite to the equal angles of a triangle are equal. Proof: In a triangle ABC, base angles are equal and we need to prove that AC = BC or ∆ABC is an isosceles triangle.
My advice search the web for a more mathematical explanation of the isosceles triangle
