Question

PLEASE HELP I BEG I NEED JUST THIS ONE PROBLEM:
In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5. Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively. Find: BC:BN.

Please give Statement/Reasoning proof as well. THANK YOU PLEASEE

Answers

  1. For the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
    What is Trapezoid?
    A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. A trapezium is the term used in British and other varieties of English. In Euclidean geometry, a trapezoid is invariably a convex quadrilateral. The trapezoid’s parallel sides are referred to as its bases.
    Given:
    In the trapezoid ABCD ( AB ∥ CD ) point M∈ AD , so that AM:MD=3:5.
    Line l ∥ AB and going trough point M intersects diagonal AC and leg BC at points P and N respectively.
    We have to find BC:BN
    ABCD is a trapezoid and there is a point m which belongs to AD such that AM:MD=3:5.Line “l” parallel to AB intersects the diagonal AC at p and BD at N.
    Now, we know that the parallel lines divide the transversal into the segments with equal ratio, therefore, BN:NC=AM:MD
    But, BC= BN+NC
    Therefore, BC:BN = (BN + NC): BN
    ⇒ BC:BN = (3 + 5): 3
    ⇒ BC:BN = 8:3
    Hence, for the given Trapezoid ABCD the value of BC:BN is BC:BN=8:3.
    To know more about Trapezoid, click on the link
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