In the adjoining figure (not drawn to scale), PS = 4 cm, SR = 2 cm, PT = 3 cm and QT = 5 cm.

(i) Show that ΔPQR ∼ ΔPST.

(ii) Calculate ST, if QR = 5.8 cm.

In the adjoining figure, ABCD is a parallelogram in which AB = 16 cm, BC = 10 cm and L is a point on AC such that CL : LA = 2 : 3. If BL produced meets CD at M and AD produced at N, prove that :

(i) ΔCLB ∼ ΔALN.

(ii) ΔCLM ∼ ΔALB.

In the given figure, medians AD and BE of ΔABC meet at G and DF ∥ BE. Prove that :

(i) EF = FC.

(ii) AG : GD = 2 : 1.

In the given figure, DE ∥ BC and BD = DC.

(i) Prove that DE bisects ∠ADC.

(ii) If AD = 4.5 cm, AE = 3.9 cm and DC = 7.5 cm, find CE.

(iii) Find the ratio AD : DB.