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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.
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Knowledge Check

  • 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

    A
    `8 sqrt 3`cm
    B
    `8 cm`
    C
    `4sqrt3` cm
    D
    `8/sqrt3 cm`

  • 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

    A
    `8sqrt(3)cm`
    B
    8 cm
    C
    `4sqrt(3) cm`
    D
    `(8)/(sqrt(3)) cm`

  • 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.

    A
    `7 m^(2)`
    B
    `13.44 m^(2)`
    C
    `6.72 m^(2)`
    D
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