Prove that opposite sides of a parallelogram are congruent. be sure to create and name the appropriate geometric figures.

Draw a parallelogram ABCD.
Use a horizontal segment AB (A at left, B at right).
Then from B draw a segment tilting up to the right.
Call the endpoint C. Then draw a horizontal segment to the left.
Call the endpoint D. Connect D to A. Draw the sides, so that
opposite sides are parallel and ABCD looks like a parallelogram.

Given: Parallelogram ABCD
Prove: Seg AB is congr seg CD; seg AD is congr seg BC

Statements                                      Reasons
1. Parallelogram ABCD                    1. Given
2. Draw diagonal AC                        2. Construction
3. AB || DC                                       3. Def of parallelogram
4. <ACD is congr <CDB                   4. Alt int angles of || lines
5. AD || CB                                       5. Def of parallelogram
6. <DAC is congr <BCA                   6. Alt int angles of || lines
7. Seg AC is congr seg AC              7. Congruence of segs is reflexive
8. Triangle ADC is congr tri. CBA    8. ASA
9. Seg AD congr seg BC                  9. CPCTC
10. Seg. AB congr seg CD              10. CPCTC