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prove that the line segment joining the ...

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

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To prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side, we will follow these steps: ### Step-by-Step Solution: 1. **Draw Triangle and Identify Midpoints**: Let triangle ABC be given. Identify the midpoints D and E of sides AC and AB respectively. 2. **Construct a Parallel Line**: ...
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Knowledge Check

  • 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.

  • 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 .

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

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    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).

    Prove that the line segment joining the middle points of two sides of a triangle is half 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.

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