∠QPS≅∠QRS and ∠PQR≅∠PSR. Complete the proof that
QR
∥
PS
.
P
Q
R
S
T
Statement Reason
1 ∠QPS≅∠QRS Given
2 ∠PQR≅∠PSR Given
3 m∠QPS+m∠PQR+m∠QRS+m∠PSR=360° Quadrilateral Angle Sum Theorem
4 m∠QPS+m∠PQR+m∠QPS+m∠PQR=360° Substitution
5 m∠QPS+m∠PQR=180° Properties of addition, subtraction, multiplication, and division
6
QR
∥
PS
Alternate Exterior Angles Theorem
Alternate Interior Angles Theorem
Converse of Alternate Exterior Angles Theorem
Converse of Alternate Interior Angles Theorem
Converse of Corresponding Angles Theorem
Converse of Same-Side Exterior Angles Theorem
Converse of Same-Side Interior Angles Theorem
Corresponding Angles Theorem
Same-Side Exterior Angles Theorem
Same-Side Interior Angles Theorem
