# Geometry: Relationships in Triangles and Quadrilaterals

## 25 terms

### midsegment

part of a triangle that is a line segment and connects midpoints of two sides of the triangle

### coordinate proof

use variables to represent the coordinates of a figure

### midsegment theorem

midsegment is parallel to the third side and is equal to half the length of the side

### perpendicular bisector

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

### equidistant

a point that is the same distance from two figures

### perpendicular bisector theorem

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

### converse of the perpendicular bisector theorem

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

### concurrent

when three or more lines, rays, or segments intersect in the same point, they are called this

### point of concurrency

the point of intersection of the lines, rays, or segments

### concurrency of perpendicular bisectors of a triangle

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

### circumcenter

the point of the currency of the three perpendicular bisectors of a tirangle

### angle bisector

ray that divides an angle into two congruent adjacent angles

### incenter

the point of concurrency of the three angle bisectors of a triangle

### angle bisector theorem

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 theorem

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

### concurrency of angle bisectors of a triangle

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

### median

this part of a triangle is a segment from a vertex to the midpoint of the opposite side

### centroid

the point of concurrency of the three medians of a triangle; always remains inside the triangle

### altitude

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

### orthocenter

the point at which the lines containing the three altitudes of a triangle intersect

### theorem 5.10

if one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side

### theorem 5.11

if one angle of a triangle is larger than another angle, then the side opposite the smaller angle

### triangle inequality theorem

the sum of the lengths of any two sides of a triangle is greater than the length of the third side

### exterior angle inequality theorem

the measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles

### hinge theorem

if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the of the second, then the third side of the first is longer than the third side of the second