Prove that the line segments joining the midpoints of the adjacent sides of a quadrilateral form a parallelogram.

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

Prove that line segment joining the midpoints of two sides of a triangle is parallel to the third side whose length is half of the length of the third side.

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)

Prove that the line joining the orthocentre to the centroid of a triangle formed by the focal chord of a parabola and tangents drawn at its extremities is parallel to the axis of the parabola.

Find the area of a figure formed by joining the mid-points of the adjacent sides of a rhombus with diagonals 12 cm. and 16 cm.

Find the mid point of the line segment joining the points (3, 0) and (-1, 4)

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

Prove, by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the midpoint of the parallel sides (you may assume that the trapezium is not a parallelogram).

The line segment joining the mid-points of two sides of triangles is parallel to the third side and is equal to ____ of its length.

Consider square A B C D of side length 1. Let P be the set of all segments of length 1 with endpoints on the adjacent sides of square A B C D . The midpoints of segments in P enclose a region with area Adot The value of A is