Prove that , "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points then the line divides the sides in the same proportion".

Prove that , "If a line parallel to a side of a triangle intersects th

1.	Prove that , "If a line parallel to a side of a triangle intersects the remaining sides in two distinct points then the line divides the sides in the same proportion".
Answer» Proof `:` `Delta XAB ` and `Delta BAY ` have a common vertex B and their bases XA and AY lie on the same line XY. `:.` they have equal heights. `:. (A (Delta XAB))/(A ( Delta BAY )) = ( XA )/( AY ) ` …[Triangles of equal heights ] ….(1) `Delta XAB ` and `Delta ABZ ` have a common verte A and their bases XB and BZ lie on the same line XZ. `:.` they have equal heights. `:. (A( Delta XAB))/( A ( Delta ABZ)) = ( XB)/( BZ)` ....[Triangles of equal heights] ....(2) `:. Delta BAY ` and `Delta ABZ ` lie between the same two parallel lines AB and YZ. `:. ` they have equal heights, also have same base AB. `:. A ( Delta BAY ) = A ( Delta ABZ ) `.... [Triangles of equal bases and heights ] ....(3) `:.` from (1) , (2) and (3) , we get `(A(DeltaXAB))/(A(DeltaBAY)) = ( A(Delta XAB))/(A(DeltaABZ))` ....(4) `:.` from (1) ,(2) and (4) , we get `( XA)/( AY) = (XB)/( BZ)`