QUSETION四邊形QUESTION

Information provided is not sufficient to prove that AD=BC. You can construct a quadrilateral with AB=CD=5 cm. Angle ABC = Angle CDA = 60 degree, but BC = 2 and AD = 3. (The diagonal AC = sqrt19 by applying the cosine rule.) This is because angle ABC and angle CDA are not the included angle of triangle ABC and triangle ACD, although they are equal.

Consider Triangle ABC and Triangle CDA
AB =CD (given)
Angle BAC = Angle DCA (property of rectangle)
AC is the common side

Therefore Triangle ABC is equivalent to Triangle CDA (SAS)
i.e. AD = BC

By drawing the figure, you can find out that the 四邊形 is actually a //gram.
By property of //gram, the opposite sides should be equal and so AD=BC.