In △ABC, ∠B=∠C. A perpendicular AD is drawn from vertex A to side BC, meeting BC at D. Use this construction to answer the questions below.
a. (i) Show that △ABD≅△ACD by an appropriate congruence criterion.
b. (ii) Hence, prove that AB=AC.
c. (iii) If BD=4.5cm and CD=4.5cm, find the length of BC.