Home
Class 9
MATHS
B D is one of the diagonals of a quadr...

`B D` is one of the diagonals of a quadrilateral `A B C D`. `A M` and `C N` are the perpendiculars from `A\ a n d\ C` , respectively, on `B D`. Show that ar (quad. `A B C D`)=`1/2B D (A M+C N)`

Promotional Banner

Topper's Solved these Questions

  • ALGEBRAIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|247 Videos
  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

In Figure, A B C D is a rectangle. B M\ a n d\ D N are perpendicular from B\ a n d\ D respectively on A C . Prove that M B C~= D N A (ii) B M=D N

In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /_C\ a n d\ /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

In a quadrilateral A B C D ,\ C O\ a n d\ D O are the bisectors of /_C\ a n d\ /_D respectively. Prove that /_C O D=1/2(/_A+/_B)dot

In quadrilateral A B C D ,\ A O\ a n d\ B O are the bisectors of /_A\ a n d\ /_B respectively. Prove that /_A O B=1/2(/_C+/_D)dot

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A\ a n d\ C . Prove that A B=A D\ a n d\ C B=C D

In Figure, A D is a median and B L ,\ C M are perpendiculars drawn from B\ a n d\ C respectively on A D\ a n d\ A D produced. Prove that B L=C M

Diagonals of a parallelogram A B C D intersect at O. dotA L\ a n d\ C M are perpendiculars to B D such that L\ a n d\ M lie on B D . IS A L=C M ? why or why not?

The diagonals of quadrilateral A B C D ,\ A C\ a n d\ B D intersect in O . Prove that if B O=O D , the triangles A B C\ a n d\ A D C are equal in area.

If the diagonal B D of a quadrilateral A B C D bisects both /_B and /_D , show that (A B)/(B C)=(A D)/(C D) .

If the diagonal B D of a quadrilateral A B C D bisects both /_B and /_D , show that (A B)/(B C)=(A D)/(C D) .

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. If the medians of a triangle A B C intersect at G , show that a r( tr...

    Text Solution

    |

  2. D, E and F are respectively the mid-points of the sides BC, CA and AB...

    Text Solution

    |

  3. B D is one of the diagonals of a quadrilateral A B C D. A M and C N ...

    Text Solution

    |

  4. A B C D is a quadrilateral. A line through D , parallel to A C , mee...

    Text Solution

    |

  5. If the median of a △ABC intersect at G. show that ar (△AGC) = ar (△AGB...

    Text Solution

    |

  6. X Y is a line parallel to side B C of triangle A B C . If B E II AC a...

    Text Solution

    |

  7. E , F , G , H are respectively, the mid-points of the sides A B ,B C ...

    Text Solution

    |

  8. X Y is a line parallel to side B C of /\ A B C. B E || AC and C F || A...

    Text Solution

    |

  9. E , F , G , H are respectively, the mid-points of the sides A B ,B C ,...

    Text Solution

    |

  10. The side A B of a parallelogram A B C D is produced to any point Pdot ...

    Text Solution

    |

  11. Any point D is taken in the base B C of a triangle A B C\ a n d\ A...

    Text Solution

    |

  12. In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...

    Text Solution

    |

  13. In a parallelogram A B C D ,E ,F are any two points on the sides A B a...

    Text Solution

    |

  14. In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is prod...

    Text Solution

    |

  15. Prove that the area of an equilateral triangle is equal to (sqrt(3))...

    Text Solution

    |

  16. In Figure, B C || X Y ,\ B X || C A and A B || Y C. Prove that: a r( A...

    Text Solution

    |

  17. In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...

    Text Solution

    |

  18. A B C is a triangle in which D is the mid-point of BC and E is the mid...

    Text Solution

    |

  19. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

    Text Solution

    |

  20. The diagonals of a parallelogram A B C D intersect at a point O. T...

    Text Solution

    |