Thomas needs to prove the following theorem. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram
He draws the figure below and begins his proof.
ABDC
Glven:
AB II DC
Prove: ABCD is a parallelogram
Reasons
1. Given
Statements
AB DC
AB IDC
2 BACOCA
2 ?
What should be Thomas's reason for Step 2
Vertical angles are congruent
Congruent parts of congruent triangles are congruent.
of paralel lines are cut by a transversal corresponding angles are congruent
of parallel lines are cut by a transversal alternate interior angles are congruent