Home
Class 9
MATHS
A parallelogram ABCD has P the mid-point...

A parallelogram ABCD has P the mid-point of DC and Q a point of AC such that `CQ = (1)/(4) AC. PQ` produced meets BC at R. Prove that:
`PR=(1)/(2)DB`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MID-POINT AND ITS CONVERSE(INCLUDING INTERCEPT THEOREM)

    ICSE|Exercise EXERCISE 12(B)|23 Videos

  • MID-POINT AND ITS CONVERSE(INCLUDING INTERCEPT THEOREM)

    ICSE|Exercise EXERCISE 12(B)|23 Videos

  • MENSURATION (PLANE FIGURE)

    ICSE|Exercise TOPIC-3 (4 Marks Questions)|8 Videos

  • MID-POINT THEOREM

    ICSE|Exercise 4 MARKS QUESTION |15 Videos

Similar Questions

Explore conceptually related problems

A parallelogram ABCD has P the mid-point of DC and Q a midpoint of AC such that CQ = (1)/(4) AC. PQ produced meets BC at R. Prove that: R is the mid-point of BC

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

In Figure, A B C D is a parallelogram in which P is the mid-point of D C\ a n d\ Q is a point on A C such that C Q=1/4A C . If P Q produced meets B C\ a t\ R , prove that R is a mid-point of B C .

In figure, P is the mid-point of B C , ,Q is the mid-point of A P , such that B Q produced meets A C at Rdot Prove that 3RA= CA

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that : BP=2AD

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: PB=2AD

In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: O is mid-point of AP.

In trapezium ABCD, AB is parallel to DC. P and Q are the mid-points of AD and BC respectively. BP produced meets CD produced at point E. Prove that : PQ is parallel to AB.

In a parallelogram ABCD, P is a point on side AD such that 3AP = AD and Q is a point on BC such that 3CQ = BC. Prove that : AQCP is a parallelogram.

ICSE-MID-POINT AND ITS CONVERSE(INCLUDING INTERCEPT THEOREM)-EXERCISE 12(A)
  1. The following figure shows a trapezium ABCD in which AB // DC. P is th...

    Text Solution

    |

  2. The figure, given below, shows a trapezium ABCD. M and N are the mid-p...

    Text Solution

    |

  3. The figure, given below, shows a trapezium ABCD. M and N are the mid-p...

    Text Solution

    |

  4. The figure, given below, shows a trapezium ABCD. M and N are the mid-p...

    Text Solution

    |

  5. The diagonals of a quadrilateral intersect at right angles. Prove that...

    Text Solution

    |

  6. L and M are the mid-points of sides AB and DC respectively of parallel...

    Text Solution

    |

  7. ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-po...

    Text Solution

    |

  8. A parallelogram ABCD has P the mid-point of DC and Q a midpoint of AC ...

    Text Solution

    |

  9. A parallelogram ABCD has P the mid-point of DC and Q a point of AC suc...

    Text Solution

    |

  10. D, E and F are the mid-points of the sides AB, BC and CA respectively ...

    Text Solution

    |

  11. In triangle ABC, P is the mid-point of side BC. A line through P and p...

    Text Solution

    |

  12. In triangle ABC, P is the mid-point of side BC. A line through P and p...

    Text Solution

    |

  13. In trapezium ABCD, AB is parallel to DC. P and Q are the mid-points of...

    Text Solution

    |

  14. In trapezium ABCD, AB is parallel to DC. P and Q are the mid-points of...

    Text Solution

    |

  15. In a triangle ABC, AD is a median and E is mid-point of median AD. A l...

    Text Solution

    |

  16. D and F are the mid-points of sides AB and AC of a triangle ABC. A lin...

    Text Solution

    |

  17. D and F are the mid-points of sides AB and AC of a triangle ABC. A lin...

    Text Solution

    |

  18. In Delta ABC, AD is the median and DE is parallel to BA, where E is a ...

    Text Solution

    |

  19. In A ABC, E is mid-point of the median AD and BE produced meets side A...

    Text Solution

    |

  20. In the given figure, M is mid-point of AB and DE, whereas N is mid-poi...

    Text Solution

    |