Chapter 5 Geometry

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midsegments of a triangle

a segment that connects the midpoints of two sides of the triangle

midsegment theorm

the segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side

perpendicular bisecter

a segment, ray, line that is perpendicular to a segment at its midpoint

perpendicular bisector theorm

in a plane, if a point is on the perpendicular bisector of a segment, then it is equidstant from the endpoints of the segment

converse of the perpendicular bisector theorm

in a plane, if a point is equidisant from the endpoints of a segment, then it is on the perpendicular bisector of the segment

concurrent lines

three or more lines, rays, or segments that intersect at the same point

point of currency

the point of intersection

concurrency of perpendicular bisector of a triangle

the perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle

circumcenter

the point of concurrency of the three perpendicular bisectors of a trianlge (equidstant from the three vertices)

angle bisector

rays that divides an angle into two adjacent, congruent angles

angle bisector theorm

if a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

converse of the angle bisector theorm

if a point is in the interior of an angle and is equidstant from the sides of the angle, then it lies on the angle bisector of the angle

concurrency of angle bisectors of a triangle

the angle bisector of a triangle intersect at a point that is equidistant from the sides of a triangle

incenter

the poing of concurrency of the three angle bisectors of a triangle (always lies inside the triangle)

median of a triangle

a segment from a vertex to the midpoint of the opposite side

centroid

the point of concurrency of the medians (inside the two angles)

concurrency of medians of a triangle

the medians of a triangle intersect at a point that is 2/3 of the distance from the vertex to the midpoint of the opposite side

altitude

the perpendicular segment from the vertex to the opposite side or to the line that contains the opposite side

concurrency of altitudes of a triangle

the lines containing the altitudes of a triangle are concurrent

orthocenter

the point at which the lines containing the three alltitudes intersect

triangle inequality theorm

the sum of the lengthsw of any tow sides of a triangle is greater than the length of the third side

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