Show that the figure formed by joining the midpoints of sides of a rhombus successively is a rectangle.

Find the area of the triangle formed by joining the midpoints 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 .

Show that the line segments joining the midpoints of the opposite sides of a quadrilateral and bisect each other.

Prove that the line segment obtained by joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides of the trapezium.

prove that the line segment joining the midpoints of two opposite sides of a parallelogram divides the parallelogram into two parallelograms with equal area.

Two parallel lines l and m are intersected by a transversal p (see the given figure). Show that the quadrilateral formed by the bisector of interior angles is a rectangle.

Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)

Find the area of the triangle formed by the midpoint of the sides of the triangle with vertices (2,1), (-2, 3) and (4,-3).

In which of the following situations, does the list of numbers involved is in the form of a GP? (i) Salary of Sharmila, when her salary is 5,00,000 for the first year and expected to receive yearly increase of 10%. Number of bricks needed to make each step, if the stair case has total 30 steps, provided that bottom step needs 100 bricks and each successive step needs 2 brick less than the previous step. Perimeter of the each triangle, when the mid points of sides of an equilateral triangle whose side is 24 cm are joined to form another triangle, whose mid points in turn are joined to form still another triangle and the process continues indefinitely.

Prove that line segment joining mid points of the two sides of the triangle is parallel to third side.

The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.