Home
Class 12
MATHS
ABCD is a rhombus and P ,Q ,R ,S are the...

`` ABCD is a rhombus and `P ,Q ,R ,S` are the mid-points of `A B ,B C ,C D ,D A` respectively. Prove that ` P Q R S` is a rectangle.

A

trapezium

B

rhombus

C

kite

D

parallelogram

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • TRIGONOMETRIC FUNCTIONS

    NIKITA PUBLICATION|Exercise MCQs|404 Videos

Similar Questions

Explore conceptually related problems

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

A ABCD is a rhombus and P,Q,R,S are the mid-points of AB,BC,CD,DA respectively.Prove that o+PQRS is a rectangle.

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.

A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ B(-1,\ 4),\ \ C(5,\ 4) and D(5,\ -1)dot P ,\ Q ,\ R and S are the mid-points of sides A B ,\ B C ,\ C D and D A respectively. Is the quadrilateral P Q R S a square? a rectangle? or a rhombus? Justify your answer.

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

Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C 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.

ABCD is a rectangle formed by the points A(1," "1)," "B(1," "4)," "C(5," "4)" "a n d" "D(5," "1) . P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? A rectangle? or a rhombus? Justify yo

If ABCD be a rectangle and P, Q, R, S be the mid-points of AB, BC, CD and DA respectively, then the area of the quadrilateral PQRS is equal to

ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P, Q, R and S be the midpoint of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

NIKITA PUBLICATION-VECTOR-MULTIPLE CHOICE QUESTIONS
  1. Which of the following is trues?

    Text Solution

    |

  2. Which of the following is true regarding the diagonals of a parallelog...

    Text Solution

    |

  3. ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,...

    Text Solution

    |

  4. In quadrilateral ABCD, if overline(AB)=overline(CD), then it is

    Text Solution

    |

  5. In the quadrilateral ABCD :

    Text Solution

    |

  6. Let square PQRS be a quadrilateral. If M and N are the mid-points of t...

    Text Solution

    |

  7. ABCD is a quadrilateral and E is the point of intersection of the line...

    Text Solution

    |

  8. If hat(i)+hat(j)-hat(k), 2hat(i)+3hat(j), 3hat(i)+5hat(j)-2hat(k) and ...

    Text Solution

    |

  9. E and F are mid-points of sides of AD and BC respectively of quadrila...

    Text Solution

    |

  10. Which of the following is trues?

    Text Solution

    |

  11. OABC is a tetrahedron D and E are the mid points of the edges vec (OA)...

    Text Solution

    |

  12. If M and N are the mid-points of the diagonals AC and BD respectively ...

    Text Solution

    |

  13. ABCD is a rhombus and P, Q, R and S are wthe mid-points of the side...

    Text Solution

    |

  14. If P, Q are the mid-points of the diagonals AC and BD of a quadrilater...

    Text Solution

    |

  15. If ABCD is a quadrilateral, then 2overline(AB)+3overline(BC)+2overline...

    Text Solution

    |

  16. If ABCD is a square, then bar(AB) + 2 bar(BC) + 3 bar(CD) + 4 bar(DA...

    Text Solution

    |

  17. ABCD is a parallelogram with AC and BD as diagonals. Then, A vec C - ...

    Text Solution

    |

  18. Let ABCD is a parallelogram and vecAC, vecBD be its diagonal, then vec...

    Text Solution

    |

  19. ABDC is a parallelogram and P is the point of intersection of its diag...

    Text Solution

    |

  20. ABCD is a parallelogram and O is the point of intersection of its diag...

    Text Solution

    |