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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