The prove, segment AB is parallel to segment DC. is achieved using Alternate interior angles are equal
How to complete the proof
The two column proof is written as follows
Statement Reason
AB ≅ DC given
AD ≅ BC given
AC ≅ AC Reflexive property
Δ ADC ≅ Δ ABD SSS congruence theorem
∠ 1 ≅ ∠ 2 CPCTC
AB || DC Alternate interior angles are equal (∠ 1 ≅ ∠ 2)