Proposed Problem
Click the figure below to see the complete problem 380 about Triangle, Excenter, Parallel to a side, Angle, Congruence.
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Complete Geometry Problem 380
Level: High School, SAT Prep, College geometry
Wednesday, October 28, 2009
Problem 380. Triangle, Excenter, Parallel to a side, Angle, Congruence
Labels:
angle,
angle bisector,
congruence,
excenter,
isosceles,
parallel,
triangle
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AE as bisector, and AC // FE give AF = FE, so have to prove CG = GE
ReplyDeleteCE is bisector of ang GCP ( EP perpendicular to AC )
=> ang GCE = ang ECP (1)
ang ECP = ang CEG (2) ( CP // GE )
from 1 and 2
ang GCE = ang GEC
=> GC = GE
Isosceles Tr. AFE => AF=FE
ReplyDeleteIsosceles Tr. CGE => CG=GE
FG=FE-GE=AF-CG