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.
a. (i) State the two equalities that are given in the problem.
b. (ii) Using the stated equalities, write a paragraph-style proof to show that DE=DC.
c. (iii) What kind of triangle is △DCE on the basis of your result in part (ii)? Justify your answer briefly.