Question 7:
Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).
Answer:
Consider the given figure in which PQ is a line segment drawn through the mid-point P of line AB, such that PQ ∥ BC
By using basic proportionality theorem, we obtain
AQ/QC = AP/PB
AQ/QC = 1/1 (P is the mid – point of AB. ∴ AP = PB)
⇒ AQ = QC
Or, Q is the mid-point of AC.
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