Question

complete the proof that ∠rqt≅∠qrt.
statement reason
1 ∠pst≅∠spt given
2 qr || ps given
3 ∠spt≅∠qrt alternate interior angles theorem
4 ∠rqt≅∠pst alternate interior angles theorem
5 ∠spt≅∠rqt transitive property of congruence
6 ∠rqt≅∠qrt

Explanation:

Step1: Recall transitive property

We know from statements 3 ($\angle SPT\cong\angle QRT$) and 5 ($\angle SPT\cong\angle RQT$).

Step2: Apply transitive property

If $\angle SPT\cong\angle QRT$ and $\angle SPT\cong\angle RQT$, then by the transitive property of congruence, $\angle RQT\cong\angle QRT$.

Answer:

Transitive Property of Congruence