By corresponding angles we know that 1 & 4 are congruent.
By alternant interior angles we know that 2 & 5 are congruent.
I have no idea how to start this, let alone finish it. The worst part is I have to solve it by the end of tonight! Would one of you guys please help me?
Oh yeah: can I assume triangle BST is an equilateral triangle?
Solve using a two column proof:
Given: Line segment AS is parallel to line segment BT;
The measure of angle 4 is equal to the measure of angle 5
Prove: Ray SA bisects angle BSR
Set angle 5 = x
Angle 5 = Angle 4 (Given)
Angle 4 = x
Angle 3 = 180 - 2x (interior angles of a triangle)
Angle 2 = Angle 5 = x (Parallel lines, alternant interior angles)
Angle 1 = 180 - (Angle 2 + Angle 3)
Angle 1 = 180 - (x + (180 - 2x))
Angle 1 = x
Since angle 1 = angle 2, the line bisects the angle
I'll let you supply the reasons.
We see that: . .
is an exterior angle of .
. . Hence: .
Since , we have: . .
Equate  and : . .
Since . (alt-int. angles),
. .  becomes: .
and we have: .
Therefore, bisects .