Final answer:
Option D.
The student is asked to prove that SM bisects ∠RST and the correct answer is option d, which states that ∠SMR = ∠MRT, the alternate exterior angles, showing that SM is indeed the bisector of ∠RST.
Step-by-step explanation:
To prove that SM bisects ∠RST, we must demonstrate that ∠SMR equals ∠MRT.
Given the parallel lines ARB and TSC, and knowing that RT bisects ∠BRS, we can infer properties about the angles formed.
Here are the options evaluated:
- ∠SMT = ∠MRT (Vertically opposite angles) - This doesn't help prove that SM bisects ∠RST because it discusses vertically opposite angles.
- ∠STM = ∠MRS (Alternate interior angles) - This is also not directly related to proving that SM is the bisector of ∠RST.
- ∠SMR = ∠MRS (Corresponding angles) - This statement is incorrect because SM and RS are not parallel lines, hence cannot have corresponding angles.
- ∠SMR = ∠MRT (Alternate exterior angles) - This is the correct option, as alternate exterior angles are equal when lines are parallel, which helps to conclude that SM is the bisector of ∠RST.
The correct statement that proves SM bisects ∠RST is the equality of alternate exterior angles, ∠SMR = ∠MRT, which can be concluded due to the parallel lines ARB and TSC.
Therefore, the final answer in 20 words: Please mention correct option in final answer:
Option d (∠SMR = ∠MRT) is the correct choice to prove SM bisects ∠RST.