Using Converse of basic proportionality theorem, prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side
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
Proof: D is the mid point of AB (Given)
∴ AD=DB
⇒ AD/BD = 1 ... (i)
Also, E is the mid-point of AC (Given)
∴ AE=EC
⇒AE/EC = 1 [From equation (i)]
From equation (i) and (ii), we get
AD/BD = AE/EC
Hence, DE || BC [By converse of Basic Proportionality Theorem]
