1. 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

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

3. 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

4. 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

5. 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