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Pythagorean Theorem

c²\=a²+b²

if c²\=a²+b², then triangle ABC is \__________

a right triangle

if c²

acute

if c²\>a²+b² then triangle ABC is \_____________

obtuse

45-45-90 Triangle Theorem

hypotenuse \= leg x √2

30-60-90 Triangle Theorem

hypotenuse = shorter leg x 2

longer leg = shorter leg x √2

Right Triangle Similarity Theorem: if the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are \___________ to the original triangle and to each other

similar

Geometric Mean

a/x \= x/b

Geometric Mean (Altitude) Theorem

CB² = DB x AB

AC² = AD x AB

tangent ratio

tan \= opposite/adjacent

sine ratio

opposite/hypotenuse

cosine ratio

adjacent/hypotenuse

inverse tangent

if tan A \= x, then tan-1 x \= m

inverse sine

if sin A \= y, then sin-1 y \= m

inverse cosine

if cos A \= z, then cos-1 z \= m