Wednesday, March 15, 2023

Geometry Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures. Difficulty Level: High School.

Geometry Problem 1526. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

Geometry Problem 1526: Mastering Geometry Problem-Solving: Discover the Distance Between Two Sides in a Parallelogram Using Bisectors and Distance Measures. Difficulty Level: High School.

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6 comments:

  1. Replies
    1. https://photos.app.goo.gl/csBRn4k2btFAxqn86

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  2. https://photos.app.goo.gl/GwyH5jPsyhtGKUD69

    Define point I as midpoint of AD and N is the projection of D over AB
    Note that AED is the right triangle => IE=IA=ID
    Since I is the incenter of triangle AED
    So central angle ^(EID)= 2.^(EAD)= 2u=^(NAD)
    Triangle IFE similar to AND ( case AA)
    So ND/EF=AD/IE= 2
    ND=AG=2.EF=20

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  4. Let AB, DE extended meet at U. Drop a perpendicular UP to AD, P on AD.

    Triangles AEU & AED are congruent ASA & so AU = AD
    E is midpoint of DU hence from the midpoint theorem UP = 2 X 10 = 20

    Now Triangles APU & ADG are congruent ASA (since AU = AD)
    So AG = UP = 20

    Sumith Peiris
    Moratuwa
    Sri Lanka

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  5. Let K, L be projections of E onto AB, CD, then E being onto the angles bisectors, KE=EF=EL=10, but K-E-L are collinear...

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