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Problem 354. Rhombus, Square, 45 degrees.
Level: High School, College, SAT Prep.

The figure shows a rhombus ABCD with the square BCEF. If G is the intersection point of AC and DE prove that the measure of the angle AGD is 45 degrees.

Rhombus, Square

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Art of problem 354



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 ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

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