question_answer

  Prove that, if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, the other two sides are divided in the same ratio.

Answer:

  Given  in which a line parallel to sideintersects other two sides  and  at  and respectively. To prove                                      (1/2) Construction Join  and  and then draw and  Proof Area of So,   and     Similarly, and      Therefore, ?(i)(1) and    ?(ii)(1) Now, and  are on the same base and between the same parallel linesand  So,                 ...(iii) (1) Therefore, from Eqs. (i), (ii) and (iii), we have                                                      (1/2) Hence Proved