Given: line ab is congruent to line cd and line ad is congruent to line bc. prove: angle d is congruent to angle b

AD = BC > Parallel lines
AC = AC > Reflexive property
<A = <C > Congruent angles
<D = <B > Congruent angles

Ac congruent to ac by reflexive property
Triangle acd is congruent to triangle cab by side, side, side
Angle d is congruent to angle b by cpctc (corresponding parts of congruent triangles are congruent) hope this helpef