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

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

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).

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.

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.

Prove that the ratio of altitudes of two similar triangles is equal to the ratio of their corresponding sides.

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 ratio of the areas of two similar triangles is equal to the ratio of the squares of the bisectors of the corresponding angles of the triangles. [The end-points of the angular bisectors are on the opposite sides of the angles.]

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.