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Theorem 7.7 : In any triangle, the side ...

Theorem 7.7 : In any triangle, the side opposite to the larger (greater) angle is longer

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Let us assume `AC>AB`
then `/_B>/_C`
Which contradicts our assumption.
Hence, `AB>AC`.
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Knowledge Check

  • In any triangl, the side opposite to the greater angle is longer. In a DeltaABC , if angleA=45^(@), angleB=70^(@) . The largertst side of a triangle is

    A
    BC
    B
    AB
    C
    AC
    D
    None of these

  • In any triangl, the side opposite to the greater angle is longer. In DeltaABC if angleC gt angleB then

    A
    `BC gt AC`
    B
    `AB gt AC`
    C
    `AB lt AC`
    D
    `BC lt AC`

  • The side opposite to an obtuse angle of a triangle is :

    A
    smallest
    B
    greatest
    C
    half of the perimeter
    D
    none of these

    • Similar Questions

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    Theorem 7.6 : If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater)

    Prove the following statement. "The bisector of an angle of a triangle divides the sides opposite to the angle in the ratio of the remaining sides"

    Theorem 7.3 : The sides opposite to equal angles of a triangle are equal.

    Theorem 6.9 : In a triangle, if square of one side is equal to the sum of the squares of the other two sides, then the angle opposite the first side is a right angle.

    Find the odd statement out in relation to a triangle . A . The logest side is opposite to the greatest angle. B. The exterior angle of triangle is the sum of interior opposite angle. C. The sum of any 2 sides is greater than the 3^(rd) side. D. The sequare of one side = the sum of the squares of other tow sides .

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