In a triangle ABC, AB = 25 cm, AC = 35 cm and BC = 55 cm. Points D and E are taken on AB and AC respectively such that DE is parallel to BC and AD = 15 cm. Another pair of points F on AB and G on AC is chosen so that FG is also parallel to BC and AF = 10 cm.
Answer the following:
(i) Prove that ΔADE is similar to ΔABC.
(ii) Calculate the lengths AE and DE.
(iii) Calculate the lengths AG and FG.