Home
Class 9
MATHS
In Figure, AN and CP are perpendicular t...

In Figure, `AN` and `CP` are perpendicular to the diagonal `BD` of a parallelogram `ABCD` Prove that :
(i) ` A D N~= C B P`
(ii) `A N=C P`

Text Solution

Verified by Experts

"(i)`A D N~= C B P`
in triangle ADN and CBP,
`/_AND=/_CPB` `(90^@)`
`/_NDA=/_PBC` (since AD||CB and BD is a sector so alternate interior angles are equal)
`AD=BC`
so from AAS theorem , `A D N~= C B P`
(ii) `A N=C P`
...
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 N and C P are perpendicular to the diagonal B D of a parallelogram A B C Ddot Prove that : A D N~= C B P (ii) A N=C P

If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is DeltaAMD ≅ DeltaCNB ? Give reason.

P is any point on the diagonal BD of the parallelogram ABCD. Prove that ar (triangleAPD) = ar (triangleCPD) .

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D

In the given figure, ABCD is a parallelogram in which AN and CP are perpendiculars on diagonal BD. Prove that : (i) DeltaADN =DeltaCBP (ii) AN=CP

P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Then which of the following is true?

P\ a n d\ Q are the points of trisection of the diagonal B D of a parallelogram A B C Ddot Prove that C Q is parallel to A Pdot Prove also that A C bisects P Q

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . Show that (i) DeltaA P B~=\ DeltaC Q D (ii) A P\ =\ C Q

In Figure A B C D\ a n d\ A E F D are two parallelograms. Prove that: P E=F Q

Two points X and Y lie on the diagonal BD of a parallelogram ABCD such that DX = BT. Prove that squareAXCY is a parallelogram.

RD SHARMA-QUADRILATERALS-All Questions
  1. ABCD is a parallelogram and line segments AX ,CY bisect the angles A a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |