Revised GRE Geometry Math Formulas cheet sheet

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GRE

Revised GRE Geometry Math Formulas

Angles

-A right angle is made up of 90 degrees

-A straight line is made up of 180 degrees.

-If two lines intersect, the sum of the resulting four angles equals 360.

Polygons

-A polygon is any figure with three or more sides (e.g., triangles, squares, octagons, etc.).

-Total degrees = 180 (n-2), Where n=# of sides

-Average degrees per side or degree measure of congruent polygon = 180 (n-2)/n

Triangles

-Area = 1/2 (b * h)

-An isosceles right triangle (45-45-90) has sides in a ratio of x : x : x√2

-A 30-60-90 triangle has sides in a ratio of x:x√3:2x, with the 1x side opposite the 30 degree angle.

-An equilateral triangle has three equal sides. Each angle is equal to 60 degrees

-Any given angle of a triangle corresponds to the length of the opposite side. The larger the degree measure of the angle, the larger the length of the opposite side.

-A right triangle has a right angle (a 90 degree angle); the side opposite the right angle is called the hypotenuse, and is always the longest side.

-For a right triangle with legs A and B and hypotenuse C: A^2 + B^2 = c^2 This is called the Pythagorean Theorem.

-Each side of certain right triangles are integers. These sets of numbers are called Pythagorean triples, and you should memorize some of them: 3-4-5, 5-12-13, 8-15-17, 7-24-25. A multiple of a Pythagorean triple is a Pythagorean triple (e.g., 6-8-10).

-The length of the longest side can never be greater than the sum of the two other sides.

-The length of the shortest side can never be less than the positive difference of the other two sides.