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Online Geometry Problem 1076: Square, 45 Degrees, Angle, Sum, Distance, Auxiliary Construction. Level: High School, Honors Geometry, College, Mathematics Education

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In the figure ABCD is a square and the measure of angle EAF is 45 degrees. Prove that EF = BE + DF.

 

Geometry Problem: Square, 45 degrees


 

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." 
 


 

Mind Map: George Pólya's 1945 book, "How to Solve It"

George Pólya's 1945 book "How to Solve It, A new aspect of Mathematical Method", is a book describing methods of problem solving. It suggests the following steps when solving a mathematical problem: (1) First, you have to understand the problem. (2) After understanding, then make a plan. (3) Carry out the plan. (4) Look back on your work. How could it be better?
A mind map is a diagram used to visually organize information, knowledge, concepts or ideas.
 

College Geometry: Mind Map: George Pólya's 1945 book, How to Solve It
 

 

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Solution / Comment to Geometry Problem 1076
Last updated: Jan 21, 2015