Angle bisector
a line which cuts an angle into two equal halves
Incenter of a triangle
point where the three angle bisectors of a triangle meet
Point of concurrency
point where three or more lines intersect
perpendicular bisector
a line which cuts a triangle into two equal parts at 90 (degrees)
circumcenter of a triangle
the point where three perpendicular bisectors of a triangle meet
median of a triangle
a line joining a vertec to a midpoint of the opposite side
Centroid of a triangle
the point where the three medians of a triangle intersect; AKA "center of gravity
Centroid Theorem
The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side
altitude of a triangle
the perpendicular distance from one side to the opposite vertex
orthocenter of a triangle
the point where the three altitudes of a triangle intersect
midsegment of a triangle
a line segment joining the midpoints of two sides of a triangle
inscribed
a figure in which every vertex lies on a circle
circumscribed
a figure in which each side of a polygon is tangent to the circle
equidistant
a point that is the same distance rom two or more objects is said to be...
perpendicular bisector theorem
if a point if on the perpendicular bisector of a segment, then it is equidistance from the endpoints of the segment
converse of the perpendicular bisector theorem
if a point if equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
angle bisector theorem
if a point is on the bisector of an angle, then it is equidistance from the sides of the angle
converse of the angle bisector theorem
if a point is in the interior of an angle is equidistance from the sides of the angle, then it is on the bisector of the angle
incenter theorem
the inceneter of a triangle is equidistant from the sides of the triangle
triangle midsegment theorem
a midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side
indirect proof
proof by contradiction
triangle inequality theorem
the sum of any two side lengths of a triangle is greater than the third side length
hinge theorem
if two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is acrosse from the larger included angle
Pythagorean Triple
a set of three nonzero whole numbers a, b, and c such that a (squared) + b (squared) = c (squared)