Given ad = bc and ad = bc prove abcd is a parallelogram

See below

Step-by-step explanation:

Proof:

Statements                                     |  Reasons

AD ≅ BC                                         | Given

AD ║ BC                                         | Given

AC ≅ AC                                         |  Reflexive Property

∠DAC ≅ ∠ACB                               | If 2 || lines are cut by a trans., the                      

                                                       |  alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA                              | S.A.S  Postulate

BA ≅ DC                                        | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm             | If a quad. has its opposite sides

                                                      | congruent, the quad. is a parallelogram.

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