Geometry Chapter 6 Vocabulary

concurent lines

3 or more lines that intersect at the same point

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

Converse of the Angle Bisector Theorem

If a point it equidistant from both sides of an angle, then it lies on the angle bisector

Angle Bisector Theorem

If a point lies on the bisector of an angle, it is equidistant from both sides of the angle

Triangle larger angle theorem

If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Triangle longer side Theorem

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.

S-A-S Inequality Theorem

If two sides of a triangle are congruent to two sides of another angle and the included angle is larger than the included angle of the other, then the side opposite the larger included angle is longer

S-S-S Inequality Theorem

If two sides of one triangle are congruent to two sides of another triangle and the 3rd side of #1 is longer than the 3rd side of #2, the included angle on #1 is longer than the included angle of #2

Converse of the Perpendicular Bisector Theorem

In a plane, if a point is equidistant from two endpoints of a segment, then it lies of the perpendicular bisector of that segment

Perpendicular Bisector Theorem

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

centroid theorem

The centroid of a triangle is located 2/3 of the distance from each vertex to the midpoint of the opposite side

Circumcenter Theorem

The circumcenter of a triangle is equidistant from the vertices of the triangle

Incenter Theorem

The incenter of a triangle is equidistant from the sides of the triangle.

orthocenter

The point of concurrency of the altitudes of a triangle

centroid

The point of concurrency of the medians of a triangle

triangle inequality Theorem

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

perpendicular bisector

a line perpendicular to a segment that intersects the segment's midpoint

altitude of a triangle

a perpendicular segment from a vertex to the line containing the opposite side

angle bisector

a ray that divides an angle into two congruent angles

Median of a triangle

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

equidistant

same distance from each figure

midsegment of a triangle

segment that connects the midpoints of two sides of a triangle

Incenter

the point of concurrency of the angle bisectors of a triangle

circumcenter

the point of concurrency of the perpendicular bisectors of a triangle

Point of concurrency

the point of intersection of concurrent lines