Home
Class 9
MATHS
Each of the four sides of a rhombus is o...

Each of the four sides of a rhombus is of the same length.

Text Solution

Verified by Experts

Given :
A rhombus ABCD such that AB = BC.
To prove :
AB=BC=CD=DA.Proof :
Since ABCD is a rhombus.
Therefore, ABCD is a parallelogram.
⟹AB=CD and BC=AD
But, AB=BC
Therefore, AB=BC=CD=AD
Hence, all the four sides of a rhombus are equal.
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

Each of the angles of a square is a right angle and each of the four sides is of the same length.

Each of the angles of a square is a right angle and each of the four sides is of the same length

One of the four angles of a rhombus is 60^@ . If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is

One of the four angles of a rhombus is 60^(@) . If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is

The length of each of the sides of a rhombus is given as 5 m and the length of one of its diagonals is 2.8 m Find the area of the rhombus.

Say True or False : (a) Each angle of a rectangle is a right angle. (b) The opposite sides of a rectangle are equal in length. (c) The diagonals of a square are perpendicular to one another. (d) All the sides of a rhombus are of equal length. (e) All the sides of a parallelogram are of equal length. (f) The opposite sides of a trapezium are parallel.

Find the area of the field in the form of a rhombus,if the length of each side be 14cm and the altitude be 16cm.

RD SHARMA-QUADRILATERALS-All Questions
  1. A B C D is a rhombus with /A B C=56^0dot Determine /A C Ddot

    Text Solution

    |

  2. Each of the four angles of a rectangle is a right angle.

    Text Solution

    |

  3. Each of the four sides of a rhombus is of the same length.

    Text Solution

    |

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

    Text Solution

    |

  5. If A B C and D E F are two triangles such that A B ,B C are respecti...

    Text Solution

    |

  6. In Figure, A B C D is a parallelogram and X and Y are points on the ...

    Text Solution

    |

  7. In Figure, A B C is an isosceles triangle in which A B=AC. CP parellel...

    Text Solution

    |

  8. In Figure, X ,Y are the mid-points of opposite sides A B and D C of a ...

    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. Each of the angles of a square is a right angle and each of the four ...

    Text Solution

    |

  11. The diagonals of a rectangle are of equal length.

    Text Solution

    |

  12. If the diagonals of a quadrilateral bisect each other, then the qua...

    Text Solution

    |

  13. A quadrilateral is parallelogram if its opposite angles are equal.

    Text Solution

    |

  14. A quadrilateral is a parallelogram if its opposite sides are equal.

    Text Solution

    |

  15. In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...

    Text Solution

    |

  16. In figure, Show that if the diagonals of a quadrilateral are equal and...

    Text Solution

    |

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

    Text Solution

    |

  18. Show that if the diagonals of a quadrilateral bisect each other at r...

    Text Solution

    |

  19. A quadrilateral is a parallelogram, if its one pair of opposite sides ...

    Text Solution

    |

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

    Text Solution

    |