Table of Contents

Triangles

Definitions:

Isosceles triangle - base angles are the same, Equilateral - all angles are the same (60°), aka equiangular

Centroid of a triangle - center (where the lines bisecting each angle will meet)

Area of a triangle = base*height/2

Heron's formula - area of any triangle, with sides of length a, b, c, don't know height:

  1. Find semiperimeter (sp) = perimeter/2 = (a+b+c)/2
  2. area = √(sp(sp-a)(sp-b)(sp-c))

Congruent triangles

Theorems to prove triangles are congruent:

Right Triangles

area of a right triangle = 1/2*h*w

hypotenuse is the side opposite the right angle, opposite is the side opposite the given angle, adjacent is the side next to the given angle

SOHCAHTOA (pronounced "Soak a toe-ah"): Sin=Opp/Hyp, Cos=Adj/Hyp, Tan=Opp/Adj

law of sines:

sin(A)/a = sin(B)/b = sin(C)/c  (sometimes a/sin(A) = ...)

law of cosines - to find an angle when all the sides are known

cos(A) = (b² + c² - a²) / (2bc)
cos(C) = (a² + b² - c²) / (2ab), cos(B) is same pattern
  (side a is opposite angle A, etc)
rewriting it: c = √(a² + b² - 2abcos(C))

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