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..**..