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