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expain mid point theoram

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expain mid point theoram

    • Posted by Krishna Kant 8 years, 6 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Amar Kumar 8 years, 6 months ago

    Mid point Theorem : The line segment connecting the midpoints of  two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

     ABC is a triangle P is the midpoint at AB and Q is the midpoint at AC 

    Given that: AP=PB, AQ=QC.

    To prove: PQ || BC and PQ=1/2 BC

    Plan: To prove ▲ APQ ≅ ▲ QRC

    Proof steps: AQ=QC [midpoint] ∠ APQ = ∠QRC [Corresponding angles for parallel lines cut by an transversal].

    ∠PBR=∠QRC=∠APQ [Corresponding angles for parallel lines cut by an transversal].

    ∠RQC=∠PAQ [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]

    Therefore , ▲APQ ≅ ▲QRC

    so AP=QR=PB and PQ=BR=RC.

    4Thank You

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