Step 1:According to the given data construct a imaginary figure

      Given:

      ΔABC in which D and E are the mid points of AB and AC respectively

      such  that AD = BD and AE = EC.

      To Prove: DE || BC

Step 2: Use the given hints in the question to prove the required equation

            EXAMPLE: AD = BD

                                 \frac{AD}{BD} = 1.............................(1)

                                AE = EC

                                \frac{AE}{EC} = 1..............................(2)        

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

             \frac{AD}{DB} = 1, \frac{AE}{EC} = 1.

             From this we can write  \frac{AD}{DB} = \frac{AE}{EC}

Step 4: Apply the converse of basic proportional theorem

            THEOREM: If a line divides any two sides of a triangle in the same ratio

                then the line must parallel to the third side.

          EXAMPLE:  In ∆ABC,

                            ∴ DE || BC

Hence , the line joining the mid points of any two sides of a triangle is parallel to the third side....