Friday, January 2, 2009

Elearn Geometry Problem 215: Quadrilateral, Angle Bisectors, Cyclic Quadrilateral

Geometry Problem 215: Quadrilateral, Angle Bisectors, Cyclic Quadrilateral.

See complete Problem 215 at:
gogeometry.com/problem/p215_quadrilateral_angle_bisector_cyclic.htm

Level: High School, SAT Prep, College geometry
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4 comments:

  1. MathmanMay 11, 2009 at 3:37 AM

    angle E + angle G
    = 180 - 0.5(angle B + angle C) + 180-0.5(angle A+angle D)
    = 360 - 0.5(angle A + angle B + angle C + angle D)
    = 360 - 180 = 180 #

    ReplyDelete
  2. AnonymousNovember 20, 2009 at 8:38 AM

    angle GFB=A/2 + B/2
    angle GHC=C/2 + D/2
    => GFB + GHC = 180
    => GFE + GHE = 180

    ReplyDelete
  3. AnonymousMay 13, 2021 at 12:27 PM

    1.Sum interior angles of quadrilateral = 360 degrees
    2.Angle EFG = Angle AFB = 180 degrees - angle A / 2 - angle B / 2
    3.Angle EHG = Angle CHD = 180 degrees - angle C / 2 - angle D / 2
    4.Deducing : Angle EFG + Angle EHG = 360 degrees - 180 degrees = 180 degrees =>EFGH cyclic

    ReplyDelete
  4. MarcoMarch 5, 2023 at 1:02 AM

    From Problem 214, EFGH is a cyclic quad.

    ReplyDelete

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