Given: AD = BC and AD || BC Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
the Statements and Reasons columns.

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.