Answer:
See the proof.
Step-by-step explanation:
Conclusion | Justification
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1) Ray TQ bisects Angle PTR ; Given
2) Ray TR bisects Angle QTS ; Given
3) Angle PTQ is congruent to Angle RTQ; Definition of angle bisector
4) Angle RTQ is congruent to Angle RTS; Definition of angle bisector
5) Angle PTQ is congruent to Angle RTS; Transitive property of Congruence
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Ray TQ cuts Angle PTR into two equal angles; those angles are PTQ and RTQ.
Ray TR cuts Angle QTS into two equal angles; those angles are RTQ and RST.
The transitive property says:
If u=w and w=r, then u=r.
We have the following for 3 and 4 which implies 5 based on this transitive property:
If Angle PTQ is congruent to Angle RTQ and Angle RTQ is congruent to RTS, then Angle PTQ is congruent to Angle RTS.
