Similarity in Right Triangles
Geometric means: the geometric means x between two numbers a and b is the number which satisfies the proportion.
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.
If the altitude is drawn to the hypotenuse of a right triangle, then the length of the altitude is the geometric means between the segments of the hypotenuse.
If the altitude is drawn to the hypotenuse of a right triangle, then each leg is the geometric mean between the length of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
To find out more about the similarity in triangles, read the explanation below.
Practice: Apply the theorem and corollaries relating the altitude of the right angle of a right triangle to other components of the triangle in answering the exercises below.