Answer:
See explanation
Step-by-step explanation:
Consider triangles PTS and QTR. In these triangles,
- [tex]ST=RT[/tex] - given;
- [tex]\angle SPT=\angle RQT[/tex] - given;
- [tex]\angle STP=\angle RTQ[/tex] - as vertical angles when lines PR and SQ intersect.
Thus, [tex]\triangle PTS\cong \triangle QTR[/tex] by AAS postulate.
Congruent triangles have congruent corresponding sides, so
[tex]PT=QT[/tex]
Consider segments PR and QS:
[tex]PR=PT+TR\ [\text{Segment addition postulate}]\\ \\QS=QT+TS\ [\text{Segment addition postulate}]\\ \\PT=QT\ [\text{Proven}]\\ \\ST=RT\ [\text{Given}][/tex]
So,
[tex]PR=SQ\ [\text{Substitution property}][/tex]
