Home
Class 9
MATHS
P,Q,R and S are respectively the mid poi...

P,Q,R and S are respectively the mid points of the sides AB,BC,CD and DA of a quadrilateral ABCD such that `ACbotBD`. Prove that PQRs is a rectangle.

Promotional Banner

Topper's Solved these Questions

  • QUADRILATERALS

    MODERN PUBLICATION|Exercise EXERCISE|133 Videos

  • PROBABILITY

    MODERN PUBLICATION|Exercise EXERCISE|45 Videos

  • STATISTICS

    MODERN PUBLICATION|Exercise EXERCISE|239 Videos

Similar Questions

Explore conceptually related problems

P,Q,R and S are respectively the mid points of the sides AB,BC,CD and Da of a quadrilateral ABCD in which AC=BD and ACbotBD . Prove that PQRS is a square.

D,E and F are respectively the mid points of the sides BC,CA and AB of an equilateral triangle ABC, prove that DEF is also equilateral triangle.

D, E and F are respectively the mid-points of the sides BC, CA and AB of a triangle ABC . Show that:- BDEF is a parallelogram.

ABCD is a rhombus and P, Q, R and S are ©wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

D,E and F are respectively the mid points of the sides AB,BC and CA of a triangle ABC. Prove that by joining these mid points D,E and F and the triangle ABC is divided into four congruent triangles.

P and Q are respectively the midpoints of sides AB and BC or a triangle ABC and R is the mid-point of AP, show ar(PBQ)=ar(ARC).

ABCD is a quadrilateral in which P,Q,R and S are the mid points of sides AB,BC,CD and DA respectively AC is a diagonal show that: PQRS is a parallelogram.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

P,Q,R and S are the mid-poins of the sides AB,BC,CD and DA respectively of quad. ABCD. Show that PQRS is a parallelogram such that ar(||gmPQRS) = 1/2 ar(quad.ABCD)

MODERN PUBLICATION-QUADRILATERALS-EXERCISE
  1. P,Q,R and S are respectively the mid points of the sides AB,BC,CD and ...

    Text Solution

    |

  2. Three angles of a quadrilteral are respectively 50^@ and 110^@ and 100...

    Text Solution

    |

  3. The angle of a quadrilateral are in the ratio 2: 4: 5: 7. find the ang...

    Text Solution

    |

  4. In the quad. ABCD is a point inside it. Find that OA+OB+OC+OD>AC+BD.

    Text Solution

    |

  5. In the fig. BLbotAC and DMbotAC. If BL=LM prove that AC bisects BD

    Text Solution

    |

  6. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:QB...

    Text Solution

    |

  7. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:PQ...

    Text Solution

    |

  8. In the fig. ABCD is a square and anglePQR=90^@ PB=QC=DR, prove that:an...

    Text Solution

    |

  9. ABCD is a quadrilateral whose diagonals AC and BD intersect at O, prov...

    Text Solution

    |

  10. ABCD is a quadrilateral whose diagonals AC and BD intersect at O, prov...

    Text Solution

    |

  11. A diagonal of a rectangle is inclined to one side of the rectangle at ...

    Text Solution

    |

  12. In a parallelogram, prove that sum of any two consecutive angles is 18...

    Text Solution

    |

  13. If an angle of a parallelogram is two thid of its adjacent angle, find...

    Text Solution

    |

  14. In the fig. ABCD is a parallelogram in which angleDAB=60^@ and angleDB...

    Text Solution

    |

  15. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

    Text Solution

    |

  16. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

    Text Solution

    |

  17. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

    Text Solution

    |

  18. In the fig. ABCD is a parallelogram in which angleBAO=35^@, angleDAO=4...

    Text Solution

    |

  19. The diagonals of a rhombus are perpendicular to each other .

    Text Solution

    |

  20. The diagonals of a rectangle ABCD meet at o and angleBOC=44^@ and find...

    Text Solution

    |

  21. ABCD is a rectangle with angleABD=40^@ determine angleDBC.

    Text Solution

    |