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The sides AB and AC are equal of an isos...

The sides AB and AC are equal of an isosceles triangle ABC. D E and F are the mid-points of sides BC, CA and AB respectively. Prove that:
(i) Line segment AD is perpedicular to line segment EF.
(ii) Line segment AD bisects the line segment EF.

Answer

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Knowledge Check

  • In a triangle ABC, D, E, F are the mid-points of the sides BC, CA and AB respectively , the vector vecAD is equal to

    A
    `vecBE + vecCF`
    B
    `vecBE - vecCF`
    C
    `vecCF - vecBE`
    D
    `-vecBE - vecCF`

  • In a Delta ABC, D, E, F are the mid -points of the sides BC, CA and AB respectively, the vector AD is equal to

    A
    `vec(BE) + vec(C F)`
    B
    `vec(BE ) - vec(CF)`
    C
    `vec(CF) -vec(BE)`
    D
    `-vec(BE)- vec(CF)`

  • Let D, E and F be the middle points of the sides BC,CA and AB respectively of a triangle ABC. Then, AD + BE + CF equals to

    A
    0
    B
    0
    C
    2
    D
    None of these

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