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The line joining the mid-points of two s...

The line joining the mid-points of two sides of a triangle is parallel to the third side.

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Prove that the line joining the mid-points of the two sides of a triangle is parallel to the third side.

Using Theorem 6.2 ,prove that the line joining the mid-point of any two sides of a triangle is parallel to the third side.(Recall that you have done it in class IX).

Knowledge Check

  • Assertion : If a line divides any two sides of a triangle in the same ratio , then the line is paralle to third side . Reason : Line segment joining the mid -point of any two sides of a triangle is parallel to the third side .

    A
    If both assertion and reason are true and reason is the correct explanation of assertion .
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion .
    C
    If assertion is true reason is false .
    D
    If assertion is false but reason is true .

  • Assertion : ABCD and PQRC are rectangles and Q is a midpoint of AC. Then DP = PC. Reason : The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it.

    A
    If both assertion and reason are true and reason is the correct explanation of assertion
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If assertion is false but reason is true.

  • The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half of it. In the given figure, the side AC of DeltaABC is produced to E such that CE = FAC. If D is the midpoint of BC and ED produced meets AB at F and CP, DQ are drawn parallel to BA, then FD=

    A
    `(1)/(2)FE`
    B
    `(1)/(3)EF`
    C
    2FE
    D
    FE

    • Similar Questions

    Explore conceptually related problems

    Theorem 8.9 : The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

    The line segment joining the mid-points of any two sides of a triangle is parallel to the third side of a triangle.

    Prove that the line segment joining the mid points of two side of a triangle is parallel to the third side and equal to half of it.

    The line segment joining the mid-points of any two sides of a triangle in parallel to the third side and equal to half of it.

    Prove that the line joining the middle points of the two sides of a triangle is parallel to the third side.

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