Friday, March 4, 2016

Geometry Problem 1195: Square, Two Rectangles, Congruence, Metric Relations

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Click the figure below to view more details of problem 1195.

Math: Geometry Problem 1195: Square, Two Rectangles, Congruence, Metric Relations
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3 comments:

  1. Peter TranMarch 4, 2016 at 2:31 PM

    http://s28.postimg.org/h7revidfx/Pro_1195_1.png
    Let u= EA=GK
    And v= GE=CJ
    Draw JM //BC ( M on AB ,see sketch)
    Observe that triangles GKE, JKF, JHC and HGB are similar
    And triangle JGK congruent to GJH ( per hypotenuses- legs congruence)
    So MG=HJ=GK= u and BM=CJ= v
    And GA=u+v=GB => G is the midpoint of AB => GHB is 30-60-90 triangle
    So BH= 5.sqrt(3) and CH= 10- 5.sqrt(3) and u= JH=2.CH= 20-10.sqrt(3)
    X= DJ=AG+ GM= 5+ u= 25-10.sqrt(3)

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    Replies
    1. c.t.e.oFebruary 5, 2019 at 10:54 AM

      From ∆JGK ≡ ∆GJH => MG=GK ?
      please explain

      Delete
  2. c.t.e.oFebruary 7, 2019 at 12:41 AM

    Draw GM // AD => GMJH cyclic, From GJ diameter => GMJH kite
    => G midpoint
    GB=5, BH=5√3, HC=10-5√3, FD=20-10√3, x=25-10√3

    ReplyDelete

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