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.
