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The sum of any two sides of a triangle i...

The sum of any two sides of a triangle is greater than the third side. GIVE : A `A B C`

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In` /_\ABC`,
extend AB to D in such a way that `AD=AC`. In` /_\DBC`
as the angles opposite to equal sides are always equal, so,
`/_ADC=/_ACD`
Therefore,
`/_BCD>/_BDC`
As the sides opposite to the greater angle is longer, so,
`BD>BC`
`AB+AD>BC`
Since `AD=AC` then,
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Knowledge Check

  • The sum of length of two sides of a triangle is always

    A
    less than third
    B
    greater than third
    C
    equal to third
    D
    `(2)/(3)` to third

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