1) Let ABC be a triangle in the hyperbolic plane. Let D be a point on side AB such that A*D*B and let E be a point on side AC such hat A*E*C. Prove that the sum of the measures of angles ADE and AED is greater than the sum of the measures of angles ABC and ACB. [Hint: Consider the relationship between the areas of triangles ABC and ADE. Relate this to the defects of the two triangles.]

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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1) Let ABC be a triangle in the hyperbolic plane. Let D be a point
on side AB such that A*D*B and let E be a point on side AC such
that A*E*C. Prove that the sum of the measures of angles ADE and
AED is greater than the sum of the measures of angles ABC and
ACB. [Hint: Consider the relationship between the areas of triangles
ABC and ADE. Relate this to the defects of the two triangles.]
Transcribed Image Text:1) Let ABC be a triangle in the hyperbolic plane. Let D be a point on side AB such that A*D*B and let E be a point on side AC such that A*E*C. Prove that the sum of the measures of angles ADE and AED is greater than the sum of the measures of angles ABC and ACB. [Hint: Consider the relationship between the areas of triangles ABC and ADE. Relate this to the defects of the two triangles.]
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