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