Home Geometry Mind Map Problems All Problems Visual Index Problems Art Gallery 501-510 Post a solution        By Antonio Gutierrez

Problem 506. Triangle with Three Squares, Center, Midpoint, Perpendicular, Congruence. Level: High School, College, SAT Prep.

The drawing shows a triangle ABC with the squares ABDE, BCGH and ACPQ. M is the midpoint of EG and O is the center of the square ACPQ. Prove that: (1) AMCO is another square, (2) BO and MN are congruent and perpendicular.

 

Triangle Square, Midpoint, Perpendicular, Congruence
 
  

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."

How to Solve It, Interactive Mind Map

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? 
 

Mind Map Help. To see a note: Hover over a yellow note button. To Fold/Unfold: click a branch. To Pan: click and drag the map canvas.

Problem Solving. Activate Flash plugin or Javascript and reload to view the Mind Map of How to Solve It, Interactive Mind Map, Elearning.

 

 

  Recent Additions