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

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

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
3 years ago
(r. Consider triangle ACD, 121 S and R are mid-points of sides AD and DC respectively. •••(i) [Line segment joining mid-points of two sides of a triangle is parallel to the third and half of it.] (ii) Consider triangle ABC, P and Q are mid-points of sides AB and BC respectively. 1 :. PQ II AC and PQ = -AC 2 •••(ii) [Reason same as above] From (i) and (ii), SR 11 AC and PQ II AC SR 11 PQ ...(iii) and• . SR = iAc and PQ = iAc SR = PQ. ...(iv) (iii) • SR 11 PQ and SR = PQ. [From (iii) and (iv>1 PQRS is a parallelogram. We know that diagonals of a parallelogram bisect each other, i.e., OP = OR and OQ = OS. Hence, line segments joining mid­ points of opposite sides of a quadrilat.eral bisect each other.

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