Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side.. (Recall that you have proved it in class IX).

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

Prove that the line segment joining the middle point of two sides of a triangle is parallel to the third side.

Prove that line segment joining the middle points of two non-parallel sides of a trapezium is parallel to the parallel sides.

prove by using the principle of similar triangles that: if a line segment divides two sides of a triangle proportionally, then it is a parallel to the third side.

prove by using the principle of similar triangles that: the line segment drawn parallel to the side of a triangle divides the other sides proportionally.

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angle triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides.

Find the area of the triangle formed by joining the mid-points of the sides of the triangle whose vertices are (0,-1),(2,1) and (0,3).Find the ratio of this area to the area of the given triangle.

If a line drawn parallel to one side of an acute angle triangle to intersect the other two sides at two distinct points ,then using trigonometric ratios prove that the other two sides are divided in the same ratio.

If two sides and the median drawn to one of these two sides of a trlangle are proportional to the corresponding sides and median of another triangle,prove that the two triangles are similar.

Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.