Similarity in Right Triangles

Right Triangle Similarity Theorem

If the altitude is drawn to the hypotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.

Triangle Angle Bisector Theorem

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

geometric mean

a/x=x/b so x^2=ab and x = sqrt of ab

Three Parallel Lines Theorem

If 3 parallel lines intersect 2 transversals, then they divide the transversals proportionally

Side Splitter Theorem

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Geometric Mean (Leg) Theorem

The length of each leg of the right triangle is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse that is adjacent to the leg.