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.

Converse of Basis proportionality theorem : If a line divides any two sides of a triangle in the same ratio; then the line must be parallel to the third side.

Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

Sum of any two sides of a triangle is greater than the third side.

Sum of any two sides of a triangle is not less than the third side

Prove that any two sides of a triangle are together greater than twice the median drawn to the third side.

The sum of ny two sides of a triangle is greater than third side.

Prove that sum of any two sides of a triangle is greater than twice the median with respect to the third side.

Using Theorem 6.2 ,prove that the line joining the mid-point of any two sides of a triangle is parallel to the third side.(Recall that you have done it in class IX).