coordinate proof: Line segment OS is parallel to RT. Prove

[footballted]

Given: Line segment OS is parallel to line segment RT.
Prove: Ray OS bisects angle TOR.

I need to write a plan for a proof. Help, please!

 

[stapel]

Is there maybe a drawing that goes with this, that might explain the relationships between O, S, R, and T? I was able to draw a picture:

O       R
 *-----*
 |\    |
 |  \  |
 |    \|
 *     *
S       T

...which appears to fulfill the "givens" but does not allow for the "prove", is why I ask.

Thank you.

Eliz.

 

[soroban]

Re: coordinate proof: Line segment OS is parallel to RT. Pro

Hello, footballted!

I too need a diagram or description . . .

Given: Line segment OS is parallel to line segment RT.
Prove: Ray OS bisects angle TOR.

I tried a variety of sketches . . .

           O*-------*S
           /  \
          /     \
         /        \
        /           \
       /              \
     R*-----------------*T

And I still don't know how OS will bisect angle TOR.

 

[footballted]

The drawing by Stapel is the correct one. I am not sure how to draw on this message board. thanks!

 

[stapel]

The drawing by Stapel is the correct one.

The drawing shows that Ray OS does NOT bisect angle TOR. There remains nothing to prove.

Eliz.