Question

AB|| PQ|| CD, AB=x units ,CD=y units and PQ=z units ,prove that 1/x+1/y=1/z.

Answer 1

Answer:

Step-by-step explanation:

ΔABD and ΔPQD are similar, as the corresponding sides are parallel.

      x / z = BD / QD   =>  1/x = QD /(z * BD)

ΔCDB and ΔPQB are similar, as corresponding sides are parallel.

     y / z = BD / BQ   =>  1/y = BQ / (z * BD)

Add the two equations: 

         1/x + 1/y = (BQ + QD) / (z * BD) = 1 / z