In ΔABC, ∠ABC = ∠DAC, AB = 8 cm, AC = 4 cm and AD = 5 cm.

(i) Prove that ΔACD is similar to ΔBCA.

(ii) Find BC and CD.

(iii) Find the area of ΔACD : area of ΔABC.

In the following figure, AD and CE are medians of ∆ABC. DF is drawn parallel to CE. Prove that:

(i) EF = FB,

(ii) AG : GD = 2 : 1

The ratio between the altitudes of two similar triangles is 3 : 5; write the ratio between their:

(i) corresponding medians.

(ii) perimeters.

(iii) areas.

The ratio between the areas of two similar triangles is 16 : 25. State the ratio between their :

(i) perimeters

(ii) corresponding altitudes

(iii) corresponding medians.