In the figure, ∠PQR= ∠PRQ, then prove that ∠PQS= ∠PRT.

Match the items on the right to the items on the left.

step 1

step 2

step 3

step 4

step 5

step 6

since rays QP and RP stand on ST.

∠SQP+ ∠PQR= 180° and ∠SRP+ ∠PRT= 180°

∠PQS+ ∠PQR=180 and ∠PRQ+ ∠PRT=180

∠PQS+ ∠PQR= ∠PRQ+ ∠PRT

∠PQS+ ∠PQR= ∠PQR+ ∠PRT, from given

∠PQS= ∠PRT