#31 1 CONSTRUCTION Which steps can be used to construct AQ'R'S' congruent to AORS using the SSS Congruence Theorem? 0 Construct O'S' of length OS . 0 Construct O'M , where M is the midpoint of O'S . 0 Construct an arc of length OR with center O' . 0 Construct Q'R' parallel to O'S' of length OS . 0 Construct an arc of length SR with center S" . O Label the intersection of the two arcs R' . 0 Connect the vertices O', R', and S' with segments. 0 Construct _S'Q'T' adjacent to ZO' .\f#35 i Decide whether enough information is given to prove that the triangles are congruent. If so, state the theorem you can use. ARS V. A UTV R 5 V U T There is not enough information. There is enough information to use the AAS Congruence Theorem. There is enough information to use the ASA Congruence Theorem. There is enough information to use the SAS Congruence Theorem. #36 i CONSTRUCTION Which are steps of a construction of A/KL' congruent to A./KZ using ASA Congruence Theorem? Mark point J' on the intersection of L'K and KJ . 0 Mark point K" on the intersection of ZL' and ZJ" . 0 Construct ZL' congruent to ZL . Construct the angle bisector of ZL and name it L'K . 0 Draw the rest of the segments connecting the vertices of AJ'K'L' . 0 Construct _J' congruent to ZJ . Construct J'L' congruent to JL .#37 1 Check Solution PROOF Prove the triangles are congruent using the AAS Congruence Theorem. Given ZNKM ~ ZLMK, LL ~ ZN Prove ANMK ~ ALKM Statements Reasons 1. ZNKM ~ ZLMK, LL ~ ZN 1. Given 2. 2. 3. 3. :: LM ~ NK : LK ~ NM :: KM ~ KM : ANMK ~ ALKM #: AAS Congruence Theorem : ASA Congruence Theorem : Reflexive Property of Congruence : Symmetric Property of Congruence :: Transitive Property of Congruence#38 i COLLEGE PREP Which of the following congruence statements are true? Select all that apply. W X V O TU ~ UV D ASTV~ AXVW O ATVS AVWU 0 AVST~ AVUW