Quadrilateral ABCD is a parallelogram. Complete the statements to prove that and . Statement Reason
Quadrilateral ABCD is a parallelogram. given
and definition of a parallelogram
Draw . is a transversal that intersects two pairs of parallel lines,
and and and . drawing a line segment
∠CAB ≅ ∠ACD and ∠BCA ≅ ∠CAD
m∠CAB =m∠ACD and m∠BCA = m∠CAD
Reflexive Property of Equality
ASA criterion for congruence
and Corresponding sides of congruent triangles are congruent.

1. Congruent angles have equal measures.
2. Alternate Interior Angles Theorem
3. Alternate Exterior Angles Theorem