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Question
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. (Recall that you have done it in Class IX).
Solution
Consider the given figure in which PQ is a line segment joining the mid-points P and Q of line AB and AC respectively.
i.e., AP = PB and AQ = QC
It can be observed that
`("AP")/("PB") = 1/1`
and `("AQ")/("QC") = 1/1`
∴ `("AP")/("PB") = ("AQ")/("QC")`
Hence, by using basic proportionality theorem, we obtain
PQ || BC
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