EXAMPLE 1 Use the SAS Congruence Postulate Write

EXAMPLE 1 Use the SAS Congruence Postulate Write a proof. GIVEN BC DA, BC AD ABC PROVE CDA STATEMENTS S REASONS 1. BC DA 1. Given 2. BC AD 2. Given A 3. S 4. BCA AC DAC CA 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence

EXAMPLE 1 Use the SAS Congruence Postulate STATEMENTS 5. ABC CDA REASONS 5. 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. ANSWER MRS and MPQ are congruent by the SAS Congruence Postulate.

for Examples 1 and 2 GUIDED PRACTICE 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 SU VU. ABCD. Also, RT SU and 1. Prove that SVR UVR STATEMENTS REASONS 1. Given 2. 3. 4. SV VU SVR RV RVU VR SVR UVR 2. Definition of line 3. Reflexive Property of Congruence 4. SAS Congruence Postulate

GUIDED PRACTICE 2. Prove that for Examples 1 and 2 BSR DUT STATEMENTS REASONS 1. Given 2. BS RBS 3. RS 4. DU BSR TDU 2. Definition of line 3. Given UT DUT 4. SAS Congruence Postulate