| No radicands have perfect sqaure factors other than 1 |  |
| No radicands are fractions |  |
| No Radicals are in the denominator of a fraction |  |
No radicands have perfect sqaure factors other than 1 No radicands are fractions No Radicals are in the denominator of a fraction
Definition Geometric Mean
The geometric mean between two positive numbers a,b is the
number x such that 
Similarity Theorem: The altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse creates two triangles, both of which are similar to the original triangle and each other.
Right Triangle Altitude Theorem :
Part a: The measure of the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse is the geometric mean between the measures of the two segments of the hypotenuse.
Part b: If the altitude is drawn to the hypotenuse of a right triangle, each leg of the right triangle is the geometric mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg.
Pythagorean Theorem: In
a right triangle, the sum of the squares of the measure
of the legs equals the square of the measure
of the hypotenuse.
In the picture the above theorem states: 
If the square of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
Using the above triangle this means if then 
ABC is a right triangle.
Tests for Acute, Obtuse or Right Triangles:
In triangle ABC, if c is the longest side
of the triangle, then
Relations of sides |
Type of Triangle |
|
Acute |
|
Right |
|
Obtuse |
