Q. 7 4.2( 235 Votes )

Using Theorem 6.1, prove that a line drawn through the mid-point 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 is parallel to BC.

To Prove: PQ bisects AC
Given: PQ ll BC and PQ bisects AB
According to Theorem 6.1: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.
Now, using basic proportionality theorem, we get


 [As AP = PB coz P is the mid-point of AB]


Or, Q is the mid-point of AC
Hence proved.

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