Online GMAT Prep
 
Word Problems
Rate, Work, Mixture
Interest, Discount, Profit
Data Interpretation, Measurement
Arithmetic
Integers, Decimals, Powers, Roots
Fractions, Ratios, Proportion, Percents
Statistics, Probability, Permutations, Combinations
Range, Sets, Arithmetic Word Problems
Algebra
Linear and Quadratic Equations, Inequalities
Factoring, Exponents
Sequences
Algebraic Expressions, Functions
Geometry
Area and Perimeter
Solids, Cylinders, Polygons
Pythagorean Theorem,Special Triangle Properties
Parallel and Perpendicular Lines, Line Equations
Coordinate Geometry, Geometric Visualization
Slope, Similarity
 LESSON:  Pythagorean Theorem,Special Triangle Properties
 
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PYTHAGOREAN THEOREM

The Pythagorean Theorem is an equation that relates the lengths of the edges of a right triangle.  For a triangle with edges labeled as follows,

The Pythagorean Theorem says that a2 + b2 = c2.  To truly understand this theorem, we should look at a simple proof.  Below, we have a small square embedded in a large square.

Here, we can see that the lengths of the edges of the large and small square are (a + b) and c, respectively.  Notice that there are two ways to find the area of the large square.  The first is easy; simply square an edge of the large square.  The second way is to notice that the large square is made up of a smaller square together with four triangles.  Both methods of finding the area of the large square must yield the same result.

AreaLarge Square = (a + b)2 and AreaLarge Square = AreaSmall Square + AreaTriangles.