In triangle ABC, DE||BC and AD : DB = 2 : 3. Determine the ratio of the area triangle ADE to the area triangle ABC.

4 In Δ ABC, P, Q are points on AB and AC respectively and PQ || BC. Prove that the median AD bisects PQ.
                              5 Prove that the line joining the midpoints of the sides of the triangle form four triangles, each of which is similar to the original triangle.
                         7 One angle of a triangle is equal to one angle of another triangle and the bisectors of these equal angles divide the opposite sides in the same ratio. Prove that the triangles are similar.
                                
8 The bisector of interior angle A of a triangle AB meets BC in D and the bisector of exterior angle A meets BC produced in E. Prove that