question_answer

In the given figure, AD = BC and AD || BC. Is AB = DC? Give reasons to support your answer.

Answer:

In the given figure, it is given that             AD = BC   and     AD||BC   Now in ΔADC and ΔABC   AD = BC                     [given]   ∠DAC = ∠ACB 2   [As AD||BC and AC is transversal,   ∠DAC and ∠ACB are alternate angles]   AC = AC                     (common) So by S.A.S. congruency, we have   ΔADC = ΔABC   by c.p.c.t., AB = CD