Lesson 5.1

Front 1

Concurrent

Back 1

The or more lines that intersect at a common point

Front 2

Point of Concurrency

Back 2

The intersection of three or more lines

Front 3

Perpendicular Bisectors

Back 3

Passes through the midpoint of the segment(triangle side) and is perpendicular to the segment

Front 4

Median

Back 4

Segment whose endpoints are a vertex of a triangle and the midpoint of the side opposite the vertex

Front 5

Altitude

Back 5

A segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side

Front 6

Circumcenter

Back 6

The point of concurrency of the *perpendicular bisectors* of a triangle; the center of the largest circle that contains the triangle's vertices

Front 7

Centroid

Back 7

The point of concurrency for the *medians* of a triangle;point of the balance for any triangle

Front 8

Orthcenter

Back 8

Intersection point of the *altitudes* of triangle; no special significance

Front 9

Incenter

Back 9

The point of concurrency for the *angle bisectors* of a triangle;center of the largest circle that can be drawn inside the triangle

Front 10

Theorem 5.1

Back 10

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment

Front 11

Theorems 5.2

Back 11

Any point equidistant from the endpoints of the segments lies on the perpendicular bisector of a segment

Front 12

Theorem 5.3/Circumcenter Theorem

Back 12

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

Front 13

Theorem 5.4

Back 13

Any point on the angle bisector is the equidistant from the sides of the triangle

Front 14

Theorem 5.5

Back 14

Any point equidistant from the sides of an angle lies on the angle bisector

Front 15

Theorem 5.6/Incenter Theorem

Back 15

*The incenter of triangle is equidistant from each side of the triangle*

Front 16

Theorem 5.7/Centroid Theorem

Back 16

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