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

Prove that the line joining the midpoints of any two sides of a triang

1.	Prove that the line joining the midpoints of any two sides of a triangle is parallel to third side.
Answer» According to question it is given that ABC is a triangle in which D and E are the midpoints\xa0of AB and AC respectively.To Prove\xa0{tex}D E \\\| B C{/tex}Proof :-\xa0Since D and E are the midpoints of AB and AC respectively, we have AD = DB and AE = EC.{tex}\\therefore \\quad \\frac { A D } { D B } = \\frac { A E } { E C }{/tex}\xa0[each equal to 1].Hence, by the converse of Thales\' theorem,\xa0{tex}D E \\\| B C{/tex}.