The Ungerecht Family Tree

• Angles and Vectors
• Polygons
• Triangles
• Circles, Chords, etc
• Graphing curves, circles, etc.

The sum of angles in a polygon = 180 (n - 2), where n = number of sides. This can also be written as: 180 + 180 (n-3). (Basically you add in another triangle when adding a side to polygon)

• chord has two endpoints on a circle
• secant is a line that contains a chord, but extends beyond the circle
• Intercepted arc is the part of the circle contained within the two lines
• Central angle is angle of two lines from the center of the circle
• Inscribed/Interior angle has two points and the vertex all on the circle itself
• central angle is same as the degrees of intercepted arc

if two chords AB, CD intersect at P, then AP * PB = CP * PD

Interior angle = 1/2 of intercepted arc

all inscribed angles going to the two same points on the circle have the same angle
angle of intersecting secants theorem: 
    angle formed by the secant intersection = (opposite arc - adjacent arc)/2

An angle outside the circle with two secants (or tangents) will have an angle

that is 1/2 * (difference of the intercepted arcs)

coterminal angle - the rest of the circle outside the angle.

eg. angle of 30', the coterminal is 330'
in radians, use the absolute value.  
    2pi - |angle|, or |angle| - 2pi for the negative angle

area of an arc:

a = rad*r²/2  .... comes from a = πr² for full circle, and the 
                    proportion of a circle in the arc is rad/2π
                    so a = (rad/2π)*(πr²)

• https://www2.clarku.edu/faculty/djoyce/trig/identities.html
• 11 pages of definitions, postulates and theorems: http://www.ouchihs.org/ourpages/auto/2013/7/26/52822673/Geo-PostulatesTheorems-List.pdf

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