Question 8:
Using Converse of basic proportionality theorem, prove that the line joining the midpoints of any two sides of a triangle is parallel to the third side. (Recall that you have done it in Class IX).
Answer:
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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