Home Geometry Problems All Problems 351-360 Area of a Triangle View or post a solution 
Problem 356. Square, Point inside, Triangles, Area
Level: High School, College, SAT Prep.

The figure shows a square ABCD of area S. A point P is inside the square. If S1, S2, S3, and S4, are the areas of triangles PAB, PBC, PCD, and PAD, respectively, prove that S1 + S3 = S2 + S4 = S/2.
 

Square, triangle, area 

 


 

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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