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P, Q, R and S are respectively the midpo...

P, Q, R and S are respectively the midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD. Show that
(i) PQ||AC and ` PQ=(1)/(2) AC `
(ii) PQ||SR
(iii) PQRS is a parallelogram .

Text Solution

Verified by Experts

In `triangle ABC`, P and Q are the midpoints of AB and BC respectively.
`therefore "PQ||AC and "PQ =(1)/(2) AC`. Similarly, SR||AC.
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RS AGGARWAL-QUADRILATERALS-EXERCISE 10C
  1. P, Q, R and S are respectively the midpoints of the sides AB, BC, CD a...

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  2. A square is inscribed in an isosceles right triangle so that the squar...

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  3. ABCD is a parallelogram, E and F are the mid-points of AB and CD respe...

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  4. M and N are points on opposite sides AD and BC of a parallelogram ABCD...

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  5. In the adjoining figure, PQRS is a trapezium in which PQ||SR and M is ...

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  6. In a parallelogram PQRS, PQ = 12 cm and PS = 9 cm. The bisector of ang...

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  7. In the adjoining figure, ABCD is a trapezium in which AB||DC and P,...

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  8. In the adjoining figure, AD is a median of triangle ABC and DE||BA. Sh...

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  9. In the adjoining figure, AD and BE are the medians of triangle ABC an...

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  10. Show that the diagonals of a parallelogram divide it into four tria...

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  11. In the adjoining figure, D, E, F are the midpoints of the sides BC, CA...

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  12. Show that the quadrilateral formed by joining the mid-points of the ...

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  13. prove using vectors: The quadrilateral obtained by joining mid-poin...

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  14. Show that the quadrilateral, formed by joining the mid-points of the ...

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  15. Show that the line segments joining the mid-points of the opposite ...

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  16. The diagonals of a quadrilateral ABCD are equal. Prove that the quard...

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  17. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

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  18. The midpoints of the sides AB, BC, CD and DA of a quadrilateral ABCD a...

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