Geometry Problem 104. Angles, Triangle, Quadrilateral.
Level: High School, Honors Geometry, College,
Mathematics Education
In the figure below, given a
quadrilateral ABCD, angle ABD = 2a
, angle DBC = 90  a
, angle ADB = 2b
, and angle BDC = 90  b
. Prove that angle AEB = 90 + b  a
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FACTS AND HINTS:
Geometry problem solving is one of the most challenging skills for students to learn. When a
problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an illstructured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."
