Home
Class 9
MATHS
In Figure, P Q R S is a parallelogram, P...

In Figure, `P Q R S` is a parallelogram, `P O\ a n d\ Q O` are, respectively, the angle bisectors of `/_P\ a n d\ /_Q` . Line `L O M` is drawn parallel to `P Q` . Prove that:
(i) `P L=Q M`
(ii) `L O=O M`

Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA ENGLISH|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA ENGLISH|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

In Figure, P Q R S is a parallelogram, P O and Q O are, respectively, the angle bisectors of /_P and /_Qdot Line L O M is drawn parallel to P Qdot Prove that : P L=Q M (ii) L O=O M

P Q R S is a parallelogram. P X\ a n d\ Q Y are respectively, the perpendiculars from P\ a n d\ Q to S R\ a n d\ R S produced. Prove that P X=Q Y

In Figure, P Q R S is a square and T\ a n d\ U are, respectively, the mid-points of P S\ a n d\ Q R . Find the area of /_\ O T S\ if P Q=8\ c m .

In Figure, H E L P is a parallelogram. If O E=4c m\ a n d\ H L is 5cm more then P Edot Find O Hdot

In Figure, P Q R S is a quadrilateral and T\ a n d\ U are respectively points on P S and R S such that P Q=R Q ,\ /_P Q T=/_R Q U\ a n d\ /_T Q S=/_U Q Sdot Prove that Q T=Q Udot

In figure, A B\ a n d\ C D are straight lines and O P\ a n d\ O Q are respectively the bisectors of angles /_B O D\ a n d\ /_A O C . Show that the rays O P\ a n d\ O Q are in the same line.

P Q R S is a square such that P R\ a n d\ S Q intersect at O . State the measure of /_P O Q .

In Figure, ray O S stand on a line P O Qdot Ray O R and ray O T are angle bisectors of /_P O S\ a n d\ /_S O Q respectively. If /_P O S=x , find /_R O T

In Figure, ray O S stand on a line P O Qdot Ray O R and ray O T are angle bisectors of /_P O S\ a n d\ /_S O Q respectively. If /_P O S=x , find /_R O T

P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State the measure of /_P O Q

RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. Given /\A B C , lines are drawn through A ,\ B\ a n d\ C parallel r...

    Text Solution

    |

  2. In Figure, A N and C P are perpendicular to the diagonal B D of a para...

    Text Solution

    |

  3. In Figure, P Q R S is a parallelogram, P O\ a n d\ Q O are, respective...

    Text Solution

    |

  4. The diagonals of a parallelogram A B C D intersect at O. A line thro...

    Text Solution

    |

  5. In Figure, A B C D is a parallelogram and /D A B=60^@. If the bisector...

    Text Solution

    |

  6. In a parallelogram A B C D , the bisector of /A also bisects B C at X....

    Text Solution

    |

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

    Text Solution

    |

  8. P Q R S is a parallelogram. P X\ a n d\ Q Y are respectively, the p...

    Text Solution

    |

  9. A B C D is a parallelogram. A B is produced to E so that B E=A B . Pro...

    Text Solution

    |

  10. Two opposite angles of a parallelogram are (3x-2)^0\ a n d\ \ (50-x)...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. The perimeter of a parallelogram is 22c mdot If the longer side measur...

    Text Solution

    |

  14. In a parallelogram A B C D ,\ /D=135^0, determine the measures of /...

    Text Solution

    |

  15. A B C D is a parallelogram in which /A=70^0dot Compute /B ,\ /C\ a n...

    Text Solution

    |

  16. In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...

    Text Solution

    |

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

    Text Solution

    |

  18. A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |