Because ABCD is an isosceles trapezoid, the angles A and D are congruent.
BA and CD are congruent (given) and AD is congruent to itself (reflexive property).
Then triangles BAD and CDA form a pair of SAS triangles, so they are congruent.
BD and CA are corresponding parts in those triangles, so they are congruent (CPCTC).
7 1/2 happy early thanksgiving :)
