Home
Class 9
MATHS
The diagonals of a quadrilateral A B C D...

The diagonals of a quadrilateral `A B C D` are perpendicular. Show that the quadrilateral, formed by joining the mid-points of its sides, is a rectangle.

Text Solution

Verified by Experts

To prove-PQRS is a rectangle
Proof-
`In /_ABC`,PQ||AC and PQ=1/2AC
`In /_ADC` SR||AC and SR=1/2AC
In PQRS PQ=SR,PQRS is a parallelogram
PS||BO and PN||NO
PQ||AC and PM||QN
PMON is a parallelogram
...
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

The diagonals of a quadrilateral ABCD are perpendicular.Show that the quadrilateral, formed by joining the mid-points of its sides,is a rectangle.

Show that the quadrialteral formed by joining the mid-points of the consecutive sides of a rhombus, is a rectangle.

The diagonals of a quadrilateral ABCD are mutually perpendicular . Prove that the quadrilateral formed by joining the mid-points of its consecutive sides is a reactangle.

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.

Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a rectangle is a rhombus.

Show that the quadrilateral, formed by joining the mid-points of the sides of a square is also a square.

Show that the quadrilateral,formed by joining the mid-points of the sides of a square,is also a square.

The diagonals of a quadrilateral ABCD are equal. Prove that the quardilateral formed by joining the midpoints of its sides is a rhombus.

The quadrilateral formed by joining the mid-points of the sides AB, BC, CD, DA of a quadrilateral ABCD is

RD SHARMA-QUADRILATERALS-All Questions
  1. Show that the quadrilateral formed by joining the mid-points of the ...

    Text Solution

    |

  2. ABCD is a rhombus and P, Q ,R , S are the mid-points of AB , BC , CD ,...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  5. In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points ...

    Text Solution

    |

  6. A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D...

    Text Solution

    |

  7. P is the mid-point of side A B of a parallelogram A B C D . A line ...

    Text Solution

    |

  8. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

    Text Solution

    |

  9. Prove that the line segment joining the mid-points of the diagonals of...

    Text Solution

    |

  10. In A B C ,\ D ,\ E\ a n d\ F are, respectively, the mid-points of ...

    Text Solution

    |

  11. In a triangle /ABC ,\ /A=50^@,\ /B=60^@ and /C=70^@ . Find the measure...

    Text Solution

    |

  12. In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ ...

    Text Solution

    |

  13. In a A B C median A D is produced to X such that A D=D X . Prove that...

    Text Solution

    |

  14. In a ABC , E and F are the mid-points of AC and AB respectively. The a...

    Text Solution

    |

  15. In a A B C ,\ B M\ a n d\ C N are perpendiculars from B\ a n d\ C ...

    Text Solution

    |

  16. In Figure, triangle A B C is right-angled at Bdot Give that A B=9C M ,...

    Text Solution

    |

  17. In Figure, M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B...

    Text Solution

    |

  18. A B C is a triangle and through A ,\ B ,\ C lines are drawn para...

    Text Solution

    |

  19. In Figure, B E|A C ,\ A D is any line from A\ to\ B C intersecting B E...

    Text Solution

    |

  20. In figure A B=A C\ a n d\ C P||B A and A P is the bisector of exter...

    Text Solution

    |