Geometry

Tangent Ratio:

The length ratio of the legs of a right triangle is called the tangent ratio.

Consider the right triangle:

The tangent ratio is defined as:

Ratios, Proportions and Similarities

Geometric Means:

The geometric mean between two numbers x and z is defined as

x/y = y/z

and y is called the geometric mean of x and z.

Theorem:

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

Corollary 1:

Geometric Inequalities

Indirect Proofs:

Assume temporarily that the conclusion is false and reason logically until a contradiction of the hypothesis or another fact is reached.

Theorem:

Polygons: (polygon means "many angles")

Polygons are made by coplanar segments such that:

1. Each segment exactly intersects two other segments, one at each
endpoint.

2. No two segments with a common endpoint are collinear.

convex polygon is a polygon that has no side in the interior of the polygon.

ex.