Home
Class 9
MATHS
In a quadrilateral ABCD ,CO and DO are t...

In a quadrilateral `ABCD ,CO` and `DO` are the bisectors of `/_C` and `/_D` respectively. Prove that `/_COD=1/2(/_A+/_B)dot`

Text Solution

Verified by Experts

In a quadrilateral `ABCD ,CO` and `DO` are the bisectors of `/_C` and `/_D` respectively
from angle sum `A+B+C+D=360^@`
`A+B+2(/_1+/_2)=360^@`
`A+B+2(360^@-/_COD)=360^@`
we get `/_COD=1/2(/_A+/_B)`
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 a quadrilateral ABCD,AO and BO are the bisectors of A/_ and /_B respectively. Prove that /_AOB=(1)/(2)(/_C+/_D)

In quadrilateral ABCD,AO and BO are the bisectors of /_A and /_B respectively.Prove that /_AOB=(1)/(2)(/_C+/_D)

In a quadrilateral ABCD, AO and BO are the bisectors of angleA and angleB respectively. Prove that angleAOB=1/2(angleC+angleD).

In a quadrilateral ABCD, AO and BO are the bisectors of angle A and angle B respectively, angle C = 70^(@) and angle D=30^(@). " Then, " angle AOB= ?

In Figure,bisectors of /_B and /_D of quadrilateral ABCD meet CD and AB produced at P and Q respectively.Prove that /_P+/_Q=(1)/(2)(/_ABC+/_ADC)

In the figure bisector of /_B & /_D of quadrilateral ABCD meet CD and AB produced at P and Q respectively. Prove that /_P+/_Q=1/2(/_ABC+/_ADC).

In the figure bisector of /_B & /_D of quadrilateral ABCD meet CD and AB produced at P and Q respectively. Prove that /_P+/_Q=1/2(/_ABC+/_ADC).

In Figure,bisectors of /_B and /_D of quadrilateral ABCD meet CD and AB produced at Pand Q respectively.Prove that : /_P+/_Q=(1)/(2)(/_ABC+/_ADC)

In a quadrilateral ABCD,cos A cos B+sin C sin D=

ABCD is a quadrilateral.The bisectors of angle A and B intersect at P, show that /_C+/_D=2/_APB

RD SHARMA-QUADRILATERALS-All Questions
  1. The angle of a quadrilateral are respectively 100^@, 98^@, 92^@ Find t...

    Text Solution

    |

  2. In a quadrilateral ABCD , the angles A , B , C and D are in the ratio ...

    Text Solution

    |

  3. In a quadrilateral ABCD ,CO and DO are the bisectors of /C and /D resp...

    Text Solution

    |

  4. The angles of a quadrilateral are in the ratio 3:5:9: 13. Find all the...

    Text Solution

    |

  5. In a parallelogram ABCD , prove that sum of any two consecutive angl...

    Text Solution

    |

  6. In a parallelogram A B C D ,/D=115^@, determine the measure of /A and ...

    Text Solution

    |

  7. In Figure, A B C D is a parallelogram. Compute the values of x\ a n ...

    Text Solution

    |

  8. In Figure, find the four angles A ,\ B ,\ C\ a n d\ D in the paralle...

    Text Solution

    |

  9. In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a...

    Text Solution

    |

  10. ABCD is a parallelogram and line segments AX ,CY bisect the angles A a...

    Text Solution

    |

  11. Given A B C , lines are drawn through A ,\ B\ a n d\ C parallel res...

    Text Solution

    |

  12. In Figure, AN and CP are perpendicular to the diagonal BD of a paralle...

    Text Solution

    |

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

    Text Solution

    |

  14. The diagonals of a parallelogram ABCD intersect at OA line through O i...

    Text Solution

    |

  15. In Figure, A B C D is a parallelogram and /D A B=60^0dot If the bisect...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |