Problem 505. Right Triangle, Cevian, Sum of Segments, Angles.
Level: High School, College, SAT Prep.

The drawing shows a right triangle ABC with a cevian BD. If angle A = 2x, angle CBD = 3x, and AB = BC + CD, find x.
A cevian is a line segment in a triangle with one endpoint on a vertex and the other endpoint on the opposite side. 
 

 
 
 

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."

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? 
 

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