Adv Geometry - Similarity in triangles

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

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

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

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

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

(a + b)/2

a/x = x/b

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

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

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

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

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

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