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Problem 553: Quadrilateral, Angles, Sum
Level: High School, College, Math Education

The figure shows a quadrilateral ABCD with angles a, b, c, and d. Prove that a + c = b + d.

Quadrilateral, Angle, Sums


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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