Proving triangles congruent , vertical angles, and perpendicular lines/bisectors .

[Jaymishelle]

Given: ray ms is the bisector of line lp
line rm is congruent to line qm
angle a is congruent to angle b .

Prove: triangle rlm is congruent to triangle qpm

 

[Mrspi]

Given: ray ms is the bisector of line lp
line rm is congruent to line qm
angle a is congruent to angle b .

Prove: triangle rlm is congruent to triangle qpm

I'm pretty sure that there was a diagram which accompanied this exercise. Since I'm not going to try to GUESS what it looks like, you'll have to provide the diagram, or at least a good description, before I'll even hazard a guess at how this proof should be constructed.

That said, you might want to review the postulates or theorems you have available to prove triangles congruent. (such as SSS, SAS, ASA, AAS) Since one of your "given" facts is that two angles are congruent, you are almost certain to use one that has an "A" in it. And remember what it means for a segment to be bisected...the bisector of a segment contains the midpoint of the segment, and the midpoint of a segment divides the segment into two congruent parts. Maybe that will help you get started.