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Question
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).
Solution
Consider the given figure in which l is a line drawn through the mid-point P of line segment AB meeting AC at Q, such that PQ || BC
By using basic proportionality theorem, we obtain
`(AQ)/(QC) = (AP)/(PB)`
`(AQ)/(QC) = 1/1` (P is the midpoint of AB ∴ AP = PB)
⇒ AQ = QC
Or, Q is the mid-point of AC.
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