Pythagorean Theorem

Remember from a previous topic that a postulate is a statement assumed to be true.  A postulate is a statement that is accepted as true without proof.  A theorem is a statement that can be proven true.  Euclidean Geometry has many postulates and theorems that are integral to understanding the course.

One of the most famous theorems in Geometry is the Pythagorean Theorem.  It is named after a famous Greek mathematician named Pythagoras and works with right triangles.  Remember the sides of a right triangle have special names.  The side opposite the right angle is called the hypotenuse. The two sides that form the right angle are called legs. 

Pythag

The Pythagorean Theorem states that the sum of the squares of the lengths of the legs equals the length of the hypotenuse squared. In otherwords,

leg2 + leg2 = hypotenuse2

Triangles are named with three points, labeled with capital letters.  The side opposite the vertex is named with the corresponding lower case letter, as in the triangle below. 

ABC

The Pythagorean Theorem for the triangle above is stated: a2 + b2 = c2.

*Note: Remember that the hypotenuse is the longest segment of a right triangle.  The longest side of a triangle is always opposite the largest angle.

 

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