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Triangles

Geometry Cheat Sheet

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Geometry
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Theorems, Conjectures, & Postulates Triangle Theorems Triangle Sum Theorem- The sum of the measures of the angles in every triangle is 180? Exterior Angle Theorem- The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Corollary to the Triangle Sum Theorem- In a right triangle, the acute angles are complementary. Base Angles Theorem ? If two sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem ? If two angles of a triangle are congruent, the sides opposite them are congruent. Corollary to the Base Angle Theorem ? If a triangle is equilateral, then it?s equiangular.

Pythagorean Theorem

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Geometry
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For use with triangles, the theorem is that A Squared + B squared = C squared. C represents the Hypotenuse and A/B represent the other two legs.

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Trigonometric Functions

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Trigonometry
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In mathematics, the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Pythagorean Theorem

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Definition The longest side of the triangle is called the "hypotenuse", so the formal definition is: In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides. So, the square of a (a²) plus the square of b (b²) is equal to the square of c (c²): a2 + b2 = c2 Sure ... ? Let's see if it really works using an example. A "3,4,5" triangle has a right angle in it, so the formula should work. Let's check if the areas are the same: 32 + 42 = 52 Calculating this becomes: 9 + 16 = 25 Yes, it works ! Why Is This Useful?

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