See complete Problem 215 at:
gogeometry.com/problem/p215_quadrilateral_angle_bisector_cyclic.htm
Level: High School, SAT Prep, College geometry
Friday, January 2, 2009
Elearn Geometry Problem 215: Quadrilateral, Angle Bisectors, Cyclic Quadrilateral
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angle E + angle G
ReplyDelete= 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 #
angle GFB=A/2 + B/2
ReplyDeleteangle GHC=C/2 + D/2
=> GFB + GHC = 180
=> GFE + GHE = 180
1.Sum interior angles of quadrilateral = 360 degrees
ReplyDelete2.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
From Problem 214, EFGH is a cyclic quad.
ReplyDelete