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Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

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Show that the line segments joining the mid- points of opposite sides of a quadrilateral bisects each other.

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Prove that the lines joining the middle points of opposite sides of a quadrilateral and the line joining the middle points of its diagonals meet in a point and bisect one another.

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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 ?