EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN BC DA, BC AD PROVE ABC CDA STATEMENTS REASONS Given BC DA S Given BC AD BCA DAC Alternate Interior Angles Theorem A AC CA Reflexive Property of Congruence S

EXAMPLE 1 Use the SAS Congruence Postulate STATEMENTS REASONS ABC CDA SAS Congruence Postulate

EXAMPLE 2 Use SAS and properties of shapes In the diagram, QS and RP pass through the center M of the circle. What can you conclude about MRS and MPQ? SOLUTION Because they are vertical angles, PMQ RMS. All points on a circle are the same distance from the center, so MP, MQ, MR, and MS are all equal. MRS and MPQ are congruent by the SAS Congruence Postulate. ANSWER

GUIDED PRACTICE for Examples 1 and 2 In the diagram, ABCD is a square with four congruent sides and four right angles. R, S, T, and U are the midpoints of the sides of ABCD. Also, RT SU and . SU VU Prove that SVR UVR STATEMENTS REASONS SV VU Given SVR RVU Definition of line RV VR Reflexive Property of Congruence SVR UVR SAS Congruence Postulate

GUIDED PRACTICE for Examples 1 and 2 Prove that BSR DUT STATEMENTS REASONS Given BS DU RBS TDU Definition of line RS UT Given BSR DUT SAS Congruence Postulate