Given that APAB , BQAB , and APBQ , which of the following proves that O is the midpoint of AB and PQ ? The figure shows two triangles O A P and O B Q with a common vertex O. Points A, O, B lie on one line. Points P, O, Q lie on one line. 1.APBQ (Given)2.APAB,BQAB (Given)3.mA=mB=90 (Def. of )4.AOOB (Rt. s Thm.)5.AOQBOP (Vert. s Thm.)6.AOPBOQ (SAS Steps 1, 5, 4)7.AOBO,OPOQ (CPCTC)8.AO=BO,BO=OQ (Def. of )9.O is the midpoint of AB and PQ.(Def. of midpoint) 1.APBQ (Given)2.APAB,BQAB (Given)3.mA=mB=90 (Def. of )4.AB (Rt. s Thm.)5.AOPBOQ (Vert. s Thm.)6.OAPOBQ (AAS Steps 4, 5, 1)7.AOBO,POOQ (CPCTC)8.AO=BO,PO=OQ (Def. of )9.O is the midpoint of AB and PQ.(Def. of midpoint) 1.APBQ (Given)2.APAB,BQAB (Given)3.mA=mB=180 (Def. of )4.AOOB (Supp. s Thm.)5.AOPBOQ (SAS Steps 1, 5, 4)6.AOOP,BOOQ (CPCTC)7.AO=OP,BO=OQ (Def. of )8.O is the midpoint of AB and PQ.(Def. of midpoint) 1.APBQ (Given)2.APAB,BQAB (Given)3.mA=mB=180 (Def. of )4.AB (Supp. s Thm.)5.AOPBOQ (Adj. s Thm.)6.OAPOBQ (AAS Steps 4, 5, 1)7.AOOP,BOOQ

P B Ab O