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Prove that the quadrilateral obtained by...

Prove that the quadrilateral obtained by successively joining the mid -points of a parallelogram is also a parallelogram.

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Prove that the quadrilateral formed by joining the mid-points successively of any quadrilateral is also a parallelogram. Also, prove that the perimeter of that parallelogram is equal to the sum of that quadrilateral's diagonals.

Prove that the quadrilateral formed by joining the mid-points of the sides of a square is also a square.

Prove that the quadrilateral formed by joining the mid-points of the sides of a rectangle is a rhombus, but not a square.

Prove that the line segment joining the mid-points of the lateral sides of any trapezium is parallel to any of its parallel sides.

By vector method show that the figure formed by joining the mid-points of a quadrilateral is parallelogram.

Using the properties of vectors, prove that the straight line, obtained by joining the mid-poings of two sides of a triangle , is half of the length of third side.

Prove that the line segment joining the mid-point of two transverse sides of a trapezium is parallel to its parallel sides.

Prove that the area of the parallelogram produced by joining the mid-points of the sides of a quadrilateral taken in order is half the area of the quadrilateral.

Prove that if each diagonal of a quadrilateral bisects it into two triangles of equal areas, then it is a parallelogram.

By vector method prove that the straight line joining the mid-points of the diagonals of a trapezium is parallel ot the parallel sides and half of their difference.

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