Home
Class 9
MATHS
A B C D is a parallelogram. L\ a n d\ M ...

`A B C D` is a parallelogram. `L\ a n d\ M` are points on `A B\ a n d\ D C` respectively and `A L=C M` . Prove that `L M\ a n d\ B D` bisect each other.

Text Solution

Verified by Experts

Here `AB=CD`(opposite sides of parallelogram)
Subtraction AL from both sides `AB−AL=CD−AL`
`AB−AL=CD−CM` (because `AL=CM`)
`LB=DM`
In triangle BLO and MDO `/_MDO=/_LBO` (because `AB∣∣CD` and taking DB as transversal)
...
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

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L C M)=a r\ ( L B M)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L O B)=a r\ (\ M O C)

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

In a parallelogram A B C D , write the sum of angle A\ a n d\ B

In a A B C , If L a n d M are points on A B a n d A C respectively such that L M B Cdot Prove that: a r ( A B M)=a r ( A C L)

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

A B C D is a parallelogram and E\ a n d\ F are the centroids of triangles A B D\ a n d\ B C D respectively, then E F= (a) A E (b) B E (c) C E (d) D E

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.

RD SHARMA-QUADRILATERALS-All Questions
  1. In Figure, A B C D is a parallelogram and /D A B=60^0dot If the bisect...

    Text Solution

    |

  2. In a parallelogram ABCD , the bisector of /A also bisects BC at X Prov...

    Text Solution

    |

  3. A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C ...

    Text Solution

    |

  4. PQRS is a parallelogram. PX and QY are respectively, the perpendicular...

    Text Solution

    |

  5. ABCD is a parallelogram. AB is produced to E so that B E=A B. Prove th...

    Text Solution

    |

  6. If A B C D is a quadrilateral in which A B C D and A D=B C , prove th...

    Text Solution

    |

  7. Two opposite angles of a parallelogram are (3x-2)^@ and (50-x)^@ Find...

    Text Solution

    |

  8. If an angle of a parallelogram is two-third of its adjacent angle, fin...

    Text Solution

    |

  9. Find the measure of all the angles of a parallelogram, if one angle is...

    Text Solution

    |

  10. The perimeter of a parallelogram is 22 cm If the longer side measures ...

    Text Solution

    |

  11. In a parallelogram ABCD , /D=135^@, determine the measures of /A and...

    Text Solution

    |

  12. A B C D is a parallelogram in which /A=70^@ Compute /B ,\ /C\ a n d\...

    Text Solution

    |

  13. In Figure, A B C D is a parallelogram in which /A=60^@ . If the bisect...

    Text Solution

    |

  14. In Figure, A B C D is a parallelogram in which /D A B=75^0a n d\ /D ...

    Text Solution

    |

  15. A B C D is a parallelogram and E is the mid-point of B C , DE and AB w...

    Text Solution

    |

  16. Which of the following statements are true (T) and which are false ...

    Text Solution

    |

  17. Show that if the diagonals of a quadrilateral bisect each other at rig...

    Text Solution

    |

  18. Show that the diagonals of a square are equal and bisect each other at...

    Text Solution

    |

  19. Show that if the diagonals of a quadrilateral are equal and bisect e...

    Text Solution

    |

  20. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

    Text Solution

    |