Q. 64.2( 43 Votes )

# Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

Answer :

To prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side.

⇒ now we know the converse of a basic proportionality theorem is if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.

⇒ Let us assume ABC in which D and E are the mid points of AB and Ac respectively such that

⇒ AD = BD and AE = EC.

⇒ To prove that DE || BC

⇒ D is the midpoint of AB

∴ AD = DB

⇒ ………eq(1)

Also, E is the midpoint of AC

∴ AE = EC

⇒ ……..eq(2)

From equation (1) and (2) we get

⇒

∴ DE || BC by converse of proportionality thereom

Hence, the line joining the mid points of any two sides of a triangle is parallel to three sides.

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