Home
Class 9
MATHS
Show that if the diagonals of a quadrila...

Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Text Solution

Verified by Experts

Take quadrilateral,` ABCD, AC \and\ BD` are diagonals which intersect at O.
In `/_\AOB and /_\AOD`
`DO=OB`( O is the midpoint)
`AO=AO`( Common side
`/_\AOB=/_\AOD`(Right angle
So,`/_\AOB~=/_\AOD`
`AB=AD`
Similarly, `AB=BC=CD=AD` can be proved which means that ABCD is a rhombus
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

If diagonal of a quadrilateral bisects each other at right angles then it is a

Prove that; If the diagonals of a quadrilateral bisect each other at right angles,then it is a rhombus.

Prove that the if the diagonals of a quadrilateral bisct each other at right angles then it is a rhombus.

If the diagonals of a quadrilateral bisect each other at right angles, then this quadrilateral is

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles,then it is a square

Show that if the diagonals of a quadrilateral are equal and bisect each other at right angle, then it is a square.

If the diagonals of a quadrilateral bisect each other at right angles, then this quadrilateral is a

Show that the diagonals of a square are equal and bisect each other at right angles.

Show that the diagonals of a square are equal and bisect each other at right angles.

RD SHARMA-QUADRILATERALS-All Questions
  1. A B C D is a parallelogram and E is the mid-point of B C , DE and AB w...

    Text Solution

    |

  2. Which of the following statements are true (T) and which are false ...

    Text Solution

    |

  3. Show that if the diagonals of a quadrilateral bisect each other at rig...

    Text Solution

    |

  4. Show that the diagonals of a square are equal and bisect each other at...

    Text Solution

    |

  5. Show that if the diagonals of a quadrilateral are equal and bisect e...

    Text Solution

    |

  6. In a triangle A B C median A D is produced to X such that A D=D Xdot P...

    Text Solution

    |

  7. In Figure, A B C D is a parallelogram and X ,Y are the mid=points of s...

    Text Solution

    |

  8. In Figure, X ,\ Y are the mid-points of opposite sides A B\ a n d\ D...

    Text Solution

    |

  9. Two segments A C and B D bisect each other at O . Prove that A B C D i...

    Text Solution

    |

  10. In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on th...

    Text Solution

    |

  11. In Figure, A B C is an isosceles triangle in which A B=A CdotC P A B a...

    Text Solution

    |

  12. A B ,C D are two parallel lines and a transversal l intersects A B at ...

    Text Solution

    |

  13. If A B C\ a n d\ D E F are two triangles such that A B ,\ B C are ...

    Text Solution

    |

  14. P Q R S is a square such that P R\ a n d\ S Q intersect at Odot State ...

    Text Solution

    |

  15. The diagonals of a rectangle A B C D\ meet at O . If /B O C=44^0, ...

    Text Solution

    |

  16. If P Q R S is a square, then write the measure of /S R P

    Text Solution

    |

  17. If A B C D is a rectangle with /B A C=32^0, find the measure of /D B C

    Text Solution

    |

  18. If A B C D is a rhombus with /A B C=56^0, find the measure of /A C D

    Text Solution

    |

  19. ABCD is a rhombus. Show that diagonal AC bisects /Aas well as /Cand d...

    Text Solution

    |

  20. ABCD is a rectangle in which diagonal AC bisects /Aas well as /C. Sho...

    Text Solution

    |