Wednesday, March 18, 2020

Dynamic Geometry Problem1463: Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

Dynamic Geometry Problem1463: Parallelogram, Interior Point, Opposite Triangles with Equal Sum of Areas, Step-by-step Illustration, iPad.
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2 comments:

  1. Sumith PeirisMarch 18, 2020 at 11:28 PM

    Draw XPY parallel to BC & AD

    If S(BPX) = x & S(CPY) = y then S(APX) = S1-x & S(DPY) = S3-y

    Easily x+y = S2 ….(1) and (S1-x) + (S3-y) = S4 …(2)

    Adding (1) + (2) gives the desired result

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete
  2. Sumith PeirisMarch 18, 2020 at 11:37 PM

    Solution 2

    Let AB = CD = a & BC = AD = b. Draw altitudes h1,h2,h3,h4 for the 4 Tr.s from P to the base

    S1 + S3 = a(h1+h3)/2 = S(ABCD)/2 and S2 + S4 = b(h2+h4) = S(ABCD)/2 and the result follows.

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete

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