Adv Geometry - Similarity in triangles

woah

AA \~ post

If 2 angles in 1 triangle are congruent to 2 angles in another triangle, the triangles are similar

SAS \~ thm

If 2 sides of 2 triangles are proportional, and the included angles are congruent, the triangles are similar

SSS \~ thm

If corresponding sides of 2 triangles are proportional, the 2 triangles are similar

Perimeter + area of similar figures thm

If the similarity ratio of two similar figures is a/b, then the perimeter ratio is a/b, and the area ratio is a^2/b^2

area + volume of similar solids thm

If the similarity ratio of two similar solids is a/b, the surface area ratios are a^2/b^2, and the ratio of volumes is a^3/b^3

Arithmetic mean

(a + b)/2

Geometric mean

a/x = x/b

Altitude on hypotenuse thm

The altitude to the hypotenuse of a right triangle divides the triangle into 2 triangles similar to each other and the original  triangle

Corollary 1 to altitude on hypotenuse thm

Right triangle with alt. to hypotenuse: AD/CD = CD/DB

Corollary 2 to altitude on hypotenuse thm

Right triangle with alt. to hypotenuse: AB/AC = AC/AD

Side-splitter thm

If a line is parallel to 1 side of a triangle and intersects the other 2 sides, it divides the sides proportionally

Corollary to side-splitter thm

If 3 parallel lines intersect 2 transversals, the segments intercepting the transversals are proportional

Triangle-angle-bisector thm

If a ray bisects an angle of a triangle, it divides the opposite side into segments proportional to the other 2 sides of the triangle