Chapter 6 vocab Warnock

notes in order of the book + some that would help (didn't finish)

Converse

the opposite of the original statement

Perpendicular Bisector Theorem

In a plane, if a point lies 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 lies on the perpendicular bisector of the segment

Angle Bisector Theorem

If a point lies 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 two sides of the angle, then it lies on the bisector of the angle.

concurrent

when three or more lines, rays, or segments intersect at one point

point of concurrency

The POINT of intersection of the lines, rays, or segments

Circumcenter

equidistant from all the vertices of the triangles

Circumcenter Theorem

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

Incenter

equidistant from the sides of the triangles

Incenter Theorem

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

Median

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

Centroid

The point of concurrency of the medians of a triangle

Centroid Theorem

The centroid of a triangle is two-thirds of the distance from each vertex to the midpoint of the opposite side.

Orthocenter

the lines containing the altitudes of a triangle are concurrent, intersecting at a point

Midsegment

segment that connects the midpoints of two sides of a triangle

Triangle Midsegment Theorem

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.

Triangle Inequality Theorem

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

relationship between angles and sides

The smallest side in a triangle is opposite to the smallest angle, the biggest side is opposite to the biggest angle