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".

(B) Solve any two of the following subquestions : Prove that following statement, " If a line parallel to a side of a Delta intersects the remaining sides in two distinct points , then the line divides the sides in the same proportion . "

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. Using the above result, do the following: In Fig. 7 .45 DE abs() BC and BD = CE. Prove that DeltaABC is an isosceles triangle.

Theorem 6.1 : If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

'If a line is drawn to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

Basic proportionality Theorem or Thales Theorem - If a line is drawn parallel to one side of a triangle intersecting the other two sides; then it divides the two sides in the same ratio.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in disinct points, the other two sides are divided in the same ratio. Using this theoure. Find EC in if DE||BC.

If a line through one vertex of a triangle divides the opposite sides in the Ratio of other two sides; then the line bisects the angle at the vertex.

Prove that a line drawn from the vertex of a triangle to its base is bisected by the line joining the mid points of the remaining two sides of the triangle.

Theorem 6.2 : If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.