If we use this next year and want to be brief on the concurrency points, it would be better to make a table listing the types of segments and the name of the point of concurrency with a diagram. Skip the words and definitions since we are just briefly mentioning each term.

DNA Chapter 5 – 1 Bisectors, Medians, and Altitudes of Triangles pp. 269 - 278

Distance from a point to a line The length of the perpendicular segment from the point to the line. No Yes No

Perpendicular bisector is a segment, ray, line or plane that is to a segment at its midpoint.

A perpendicular bisector of a triangle bisects one of its sides.

Sample problem: Find x and y.

Perpendicular Bisector Theorem Any point on the  bisector of a segment is equidistant from the endpoints of the segment. A B P P is on the

Angle Bisector Theorem Any point on the bisector of an angle is equidistant from the 2 sides of the angle. D B A C

Altitude (height) of a Triangle The  segment from a vertex to the opposite side of the . Vertex

Median of a  A segment connecting a vertex of the triangle and the midpt of the opposite side.

P is called the point of concurrency. Concurrent Lines 3 or more lines that intersect at the same pt. l P is called the point of concurrency. P m n

The point of concurrency of the 3 of a is called the circumcenter of the

The circumcenter is the point used to circumscribe (circle) the triangle so that the circle passes through each vertex of the .

The point of concurrency of the 3  bisectors of a . Incenter The point of concurrency of the 3  bisectors of a . The incenter is the point used to construct an inscribed circle (a circle inside of a triangle).

Orthocenter The point of concurrency of the 3 altitudes of a .

Balance point of the triangle! Centroid The point of concurrency of the 3 medians of a . Balance point of the triangle!

Homework: Textbook pp. 274 – 278, problems 2, 6 – 15, and 47 – 50, and 52 - 54.