Question

Given that SQ bisects ∠PSR and PS≅SR , which of the following proves that △PQS≅△RQS ?

a. 1.PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Given)2.SQ⎯⎯⎯⎯⎯ bisects ∠PSR.(Given)3.SP⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Def. of bisect)4.SQ⎯⎯⎯⎯⎯≅SQ⎯⎯⎯⎯⎯ (Sym. Prop. of ≅)5.△PQS≅△RQS (SAS Steps 1, 3, 4)


b. 1.PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Given)2.SQ⎯⎯⎯⎯⎯ bisects ∠PSR.(Given)3.PQ⎯⎯⎯⎯⎯≅QR⎯⎯⎯⎯⎯ (Def. of bisect)4.SQ⎯⎯⎯⎯⎯≅SQ⎯⎯⎯⎯⎯ (Sym. Prop. of ≅)5.△PQS≅△RQS (SAS Steps 1, 3, 4)


c. 1.PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Given)2.SQ⎯⎯⎯⎯⎯ bisects ∠PSR.(Given)3.m∠SQP=m∠SQR (Def. of bisect)4.∠SQP≅∠SQR (Def. of ≅)5.SQ⎯⎯⎯⎯⎯≅SQ⎯⎯⎯⎯⎯ (Reflex. Prop. of ≅)6.△PQS≅△RQS (SAS Steps 1, 4, 5)


d. 1.PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Given)2.SQ⎯⎯⎯⎯⎯ bisects ∠PSR.(Given)3.m∠PSQ=m∠QSR (Def. of bisect)4.∠PSQ≅∠QSR (Def. of ≅)5.SQ⎯⎯⎯⎯⎯≅SQ⎯⎯⎯⎯⎯ (Reflex. Prop. of ≅)6.△PQS≅△RQS (SAS Steps 1, 4, 5)

Answer 1

Answer:

The correct choice is: c. 1. PS⎯⎯⎯⎯⎯≅SR⎯⎯⎯⎯⎯ (Given) 2. SQ⎯⎯⎯⎯⎯ bisects ∠PSR. (Given) 3. m∠SQP = m∠SQR (Def. of bisect) 4. ∠SQP≅∠SQR (Def. of ≅) 5. SQ⎯⎯⎯⎯⎯≅SQ⎯⎯⎯⎯⎯ (Reflex. Prop. of ≅) 6. △PQS≅△RQS (SAS Steps 1, 4, 5)

This proves that △PQS≅△RQS.

Step-by-step explanation: