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Definition: In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

http://www.mathopenref.com/constbisectangle.html

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Definition:
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

http://www.mathopenref.com/constmedian.html

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Definition: The orthocenter is the point where all three altitudes of the triangle intersect. An altitude is a line which passes through a vertex of the triangle and is perpendicular to the opposite side. There are therefore three altitudes in a triangle.

http://www.mathopenref.com/constorthocenter.html

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Definition: In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e. forming a right angle with) a line containing the base (the opposite side of the triangle). This line containing the opposite side is called the extended base of the altitude.

http://www.mathopenref.com/constaltitude.html

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Definition: The point where the three medians of the triangle intersect.

The 'center of gravity' of the triangle

One of a triangle's points of concurrency.

http://www.mathopenref.com/constcentroid.html

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Definition: One of several centers the triangle can have, the circumcenter is the point where the perpendicular bisectors of a triangle intersect. The circumcenter is also the center of the triangle's circumcircle - the circle that passes through all three of the triangle's vertices.

http://jwilson.coe.uga.edu/emat6680fa05/evans/assignment%204/assignment%204.htm

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Optional Section: Equilateral Triangle with given angle

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Optional Section: Equilateral Triangle with given angle

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Problem 14 - 16
Use given angle and the line from problem 13

http://www.mathopenref.com/constangle60.html

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Problem 12

http://www.mathopenref.com/constequilateral.html

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http://www.mathopenref.com/constcopysegment.html

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http://www.mathopenref.com/constcopyangle.html

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Parallel Lines through point NOT on line

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Parallel Lines through point NOT on line

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Problems 10-11
http://www.mathopenref.com/constparallel.html

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Perpendicular Bisector through point NOT on line

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Perpendicular Bisector through point NOT on line

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Problems 7-9

http://www.mathopenref.com/constperpextpoint.html

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Problems 4-6

http://www.mathopenref.com/constperplinepoint.html

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Definition - The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. Each point on the perpendicular bisector is the same distance from each of the endpoints of the original line segment.

Problems 1-3

http://www.mathopenref.com/constbisectline.html