Prove: Triangles ABC and CDA are congruent
AB = DC
AM = CM and BM = DM
1. ABCD is a parallelogram 1. Given
2. AB || CD; AD || BC 2. Definition of a parallelogram
3. Angles CAB and ACD are congruent 3. If lines are ||, alt. int. angles are congruent
Angles ACB and CAD are congruent
4. AC is congruent to AC 4. Reflexive property of congruence
5. Triangles ABC and CDA are congruent 5. ASA (Angle-Side-Angle) Postulate
6. AB is congruent to CD 6. Corr. parts of cong. triangles are cong. (CPCTC)
7. AB = CD 7. Definition of congruent segments
8. Angles DBA and BDC are congruent 8. If lines are ||, alt. int. angles are congruent
9. Triangles ABM and CDM are congruent 9. ASA (Angle-Side-Angle) Postulate
10. AM is congruent to CM 10. Corr. parts of cong. triangles are cong. (CPCTC)
BM is congruent to DM
11. AM = CM and BM = DM 11. Definition of congruent segments
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