Krishna
0

Step 1: According to the given data construct a figure

              

      

          NOTE: In triangle ABC D is the mid point of the side AB

                  AD = DB or   \frac{AD}{DB} = 1  (given) .........................(1)  

                        DE // BC

                      We  have to prove AE = EC


Step 2: Apply the basic proportional theorem

            THEOREM: If a line is drawn parallel to one side of a triangle to intersect

            the other two sides in distinct points, then the other two sides are divided

              in the same ratio.

          EXAMPLE:  In ∆ABC, DE || BC

                             \frac{AD}{DB} = \frac{AE}{EC}......................(2)


Step 3: Compare the equation (1) and (2)

             \frac{AD}{DB} = 1

             \frac{AD}{DB} = \frac{AE}{EC}

          From this we can write

                   \frac{AE}{EC} = 1

                  Hence proved  AE = EC