In △ABC, point D is taken on side BC such that BD=DC. A point E is chosen on segment AD so that DE=BD. Prove the following.
(i) State the two equalities that are given in the problem.
(ii) Using the stated equalities, write a paragraph-style proof to show that DE=DC.
(iii) What kind of triangle is △DCE on the basis of your result in part (ii)? Justify your answer briefly.