answer: proved ,they are congruent
Explanation:
Given that ABCD is a parallelogram, then AB = CD (opposite sides of a parallelogram). It is given that BC = AD. Therefore, triangles ABC and ADC share two equal sides, AB = CD and BC = AD.
Moreover, if <B = <D, then these triangles also share an equal angle. To see why this is true, we can extend BC and AD to intersect at point E. Since ABCD is a parallelogram, we know that <ADE = <CBE. However, since <B = <D, we know that <CBE = <ABD. Therefore, we have <ADE = <ABD, implying that triangles ABC and ADC share an equal angle.
Therefore, by the Side-Angle-Side (SAS) congruence criterion, triangles ABC and ADC are congruent.