The line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.
|1. EBCD is a parallelogram
||1. EF∥BC (given), BA∥CD (const.).
||2. Opp.sides of a parallelogram are equal.
||3. E is mid-point of AB(given).
||4. From 2 and 3.
|In △AEF and △CDF|
||5. Alt. ∠s, CD ∥BA and AC is a transversal.
|6. ∠EFA=∠DFC||6. Vert.opp.∠s.|
||7. From 4
|8. △AEF≌△CDF||8. AAS rule of ccongruency
|Hence, F is mid-point of AC.