###### Descriptions and Examples for the POV-Ray Raytracerby Friedrich A. Lohmüller Elementary Geometry for Raytracing
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Home
- POV-Ray Tutorial

- Geometrical Basics
for Raytracing

Right-angled Triangle
Pythagorean Theorem
Trigonometry Basics
Law of cosines
Equilateral Triangle
Regular Polygon
Polyhedron
Tetrahedron
Octahedron
Cube & Cuboid
Dodecahedron
Icosahedron
Cuboctahedron
Truncated Octahedron
Rhombicuboctahedron
Truncated Icosahedron
Circles
Tangent circles
Internal Tangents
External Tangents

- Geometric 3D Animations

## Right-angled Triangle (rectangled triangle)

Note: To avoid any collision with built-in identifiers and reserved words in POV-Ray,
it's strongly recommanded to use only words beginning with capital letters
for all identifiers of variables declared by the user, i.e. use "Ri" instead of "r" and use "H" instead of "h".

 Dimensions and Names The longest side is the side opposite to the right angle γ at Point C is called hypotenuse c, the other two sides are called legs or catheti (singular: cathetus) a and b. The angle α is at A and ϐ is the angle at B. α + ϐ = 90 degrees. The radius of the circumcircle: R = 1/2 * c = 1/2* d(A,B); The median theorem: A rule for all right triangles: If MAB is the midpoint of the hypotenuse c, then CMAB = ½ c. One can also say that point C is located on the circle with diameter [AB]. Conversely, if C is any point of the circle with diameter [AB], then angle at C in the triangle ABC is a right angle.
A right-angled triangle A right-angled triangle, the median theorem
Thales' theorem:
If AB is a diameter, then the angle at C is a right angle.

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 © Friedrich A. Lohmüller, 2009 www.f-lohmueller.de