△
QR
T≅
△
PS
T∠
QPS
≅
∠
PQR
P
Q
R
S
T
| Statement | Reason | |
1 | △ QR T≅ △ PS T | Given |
2 | segment PS ≅ segment QR | CPCTC |
3 | segment PT ≅ segment QT | CPCTC |
4 | segment RT ≅ segment ST | AAS ASA CPCTC Definition of congruence SAS SSS |
5 | ∠ PST ≅ ∠ QRT | CPCTC |
6 | PR = PT + RT | Additive Property of Length |
7 | QS = QT + ST | Additive Property of Length |
8 | PR = QT + ST | Substitution |
9 | PR = QS | Transitive Property of Equality |
10 | △ PQ S≅ △ QP R | SAS |
11 | ∠ QPS ≅ ∠ PQR | CPCTC |
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