`ABCD` is a convex quadrilateral. Join the corresponding trisection points of pairs of opposite sides. Prove that the area of the central quadrilateral , so formed , is `1/9` area (BCD)

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

Consider the - following statements in respect of a quadrilateral : 1. The line segments joining the midpoints of the two pairs of opposite sides bisect each other at the point of intersection. 2. The area of the quadrilateral formed by joining the midpoints of the four adjacent sides is half of the total area of the quadrilateral. Which of the statements given above is/are correct ?

Area of the quadrilaterals formed by joining the mid points of the adjacent sides of a quadrilateral is________ the area of given quadrilateral.

Prove that if both pairs of opposite sides of a quadrilateral are equal, then it is a parallelogram.

Prove that the quadrilateral formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

Prove that the quadrilateral formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

Prove that the figure formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

Prove that the figure formed by joining the mid-points of the pairs of consecutive sides of a quadrilateral is a parallelogram.

Prove that line joining the midpoints of opposite sides of a quadrilateral bisect each other.