# 5-2 to 5-4

## 21 terms

### Perpendicular Bisector

a point is equidistant from 2 objects if it is the same distance from each

### Perpendicular Bisector Theorm

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 Theorm

If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.

### Angle Bisectors

distance from a point to a line

### Angle Bisector Theorm

if a point is on the bisector of an angle, then the point is equidisntant from the sides of the angle

n/a

### Conncurent

three of more lines intersect at one point

### Point of Concurrency

The point at which they intersect

### Concurrency of Perpendicular Bisectors Theorm

Perpendicular bisectors intersect at a point that is equidistant from the verticies

### Circumcenter

the point of concurrency of the perpendicular bisectors of a triangle

### Circumcenter of a triangle can be....

INSIDE AND OUTSIDE

### Concurrency of Angle Bisectors Theorem

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

### Incenter

the point of concurrency of the angle bisector of a triangle

### Median

a segment whose endpoint are a vertex and the midpoint of the opposite side

### Centroid

point of concurrency of the medians (BALANCING POINT)

### Concurrency of Medians Theorem

The medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side.

### What is the equation of the Concurrency of Medians Theorem

find the x-coordinate of the centroid divide the sum of the x-coordinate of the vertices by 3. do the same for y

### Altitude

the perpendicular segments from a vertex of the triangle to the lind containing the opposite

### Concurrency of Altitudes Theorem

The lines containing the altitudes of a triangle are congruent.

### Orthocenter

lines that contain the altitudes of a triangle are conncurent

### Peanut Butter Cookies Are Better If Mom Cooks After Oprah

Perp. Bisectors- Circumcenter
Angle Bisectors- Incenter
Medians- Centroid
Altitudes- Orthocenter