Final answer:
To prove that PQ = SR, we use the fact that PR bisects QS and PQ is parallel to SR. From the properties of parallel lines and bisectors, we can show that PQ = SR.
Step-by-step explanation:
To prove that PQ = SR, we need to use the fact that PR bisects QS and PQ is parallel to SR. Since PR bisects QS, it divides it into two equal parts. Let's call the point where PR intersects QS as M. Now, from the given information, we have PM = MR.
Since PQ is parallel to SR, PM and MR are also parallel to them. Therefore, from the properties of parallel lines, we have PQ = MR and SR = PM.
Combining these equalities, we can conclude that PQ = SR.