Chapter 8 – QUADRILATERALS Exercise 8.2

(Q 1) ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that :
(i) SR∥AC and SR= 1/2 AC
(ii) PQ=SR
(iii) PQRS is a parallelogram

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(Q 2) ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

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(Q 3) ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

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(Q 4) ABCD is a trapezium in which AB || DC, BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

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(Q 5) In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD.

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(Q 6) Show that the line segments joining the mid-points of the opposite sides of a quadrilateral bisect each other.

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(Q 7) ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i) D is mid-point of AC
(ii) MD⊥AC
(iii) CM= MA=1/2AB

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