`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.

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 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.

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.

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.

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 . "

Thales theorem is given by a greek mathematician. According to this theorem, if a line is drawn parallel to one side of a triangle then it divides the other two sides in the same ratio. This theorem is also known as Basic Proportionality Theorem. Here, the value of x is :

If a line is drawn parallel to the base of an isosceles triangle to intersect its equal sides, prove that the quadrilateral, so formed is cyclic.

If two sides of a cyclic quadrilateral are equal, prove that the other two sides are parallel.