Q. 8 4.2( 179 Votes )

Using Theorem 6.2, 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)

Answer :

To Prove: PQ ll BC
Given: P and Q are midpoints of AB and AC
Let us take the given figure in which PQ is a line segment which joins the mid-points P and Q of line AB and AC respectively

i.e., AP = PB and AQ = QC

We observe that,



Basic Proportionality Theorem: 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.

Hence, using basic proportionality theorem we get:

PQ parallel to BC
Hence, Proved.

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