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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. - Mathematics

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).

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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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APPEARS IN

NCERT Class 10 Maths
Chapter 6 Triangles
Exercise 6.2 | Q 7 | Page 129
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