Home
Class 9
MATHS
P Q R S is a parallelogram. P X and QY a...

`P Q R S` is a parallelogram. `P X` and QY are respectively, the perpendiculars from `P` and `Q` to `S R` and `R S` produced. Prove that `P X=Q Ydot`

Text Solution

Verified by Experts

PS=QR( opposite sides of parallelogram are equal)
`/_PSR+/_QRS=180^@`
`/_PSR=180^@-/_QRS-(1)`
`/_2+/_QRS=180^@`
`/_2=180^@-/_QRS-(2)`
`/_2=/_PSR=/_1`
`In /_PYS` and `/_QRY`
PS=QR
...
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

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

P Q R S is a square. P R and S Q intersect at Odot State the measure of /_P O Qdot

P Q R S is a square. P R and S Q intersect at Odot State the measure of /_P O Qdot

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

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

P Q\ a n d\ R S are two parallel chords of a circle and lines R P\ a n d\ S Q intersect each other at O as shown in Figure. Prove that O P=O Q

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 Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

In Figure, /_Q P R=/_P Q R and M and N are respectively on sides Q R and P R of P Q R such that Q M=P N . Prove that O P=O Q , where O is the point of intersection of P M and Q Ndot

RD SHARMA ENGLISH-QUADRILATERALS-All Questions
  1. In a parallelogram A B C D , the bisector of /A also bisects B C at Xd...

    Text Solution

    |

  2. A B C D is a parallelogram. L and M are points on A B and D C respecti...

    Text Solution

    |

  3. P Q R S is a parallelogram. P X and QY are respectively, the perpendic...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. The perimeter of a parallelogram is 22c m. If the longer side measures...

    Text Solution

    |

  8. In Figure, A B C D is a parallelogram in which P is the mid-point of D...

    Text Solution

    |

  9. A B C is a triangle. D is a point on A B such that A D=1/4A B and E is...

    Text Solution

    |

  10. Show that the line segments joining the mid-points of the opposite ...

    Text Solution

    |

  11. B M and C N are perpendiculars to a line passing through the vertex A ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  14. In a parallelogram A B C D ,/D=115^0, determine the measure of /A and ...

    Text Solution

    |

  15. In a parallelogram A B C D , prove that sum of any two consecutive ang...

    Text Solution

    |

  16. A B C D is a parallelogram andline segments A X ,C Y bisect the angles...

    Text Solution

    |

  17. In a parallelogram A B C D diagonals A C and B D intersect at O and A ...

    Text Solution

    |

  18. In a parallelogram, prove that the bisectors of any two consecutive an...

    Text Solution

    |

  19. The diagonals of a parallelogram bisect each other.

    Text Solution

    |

  20. The angle bisectors of a parallelogram form a rectangle.

    Text Solution

    |