Section 1.5 Special Points in Triangles

CONCURRENT The point where 3 or more lines intersect

What are some things you already know about triangles or circles? TRIANGLES & CIRCLES What are some things you already know about triangles or circles?

PREVIOUS FACTS… How many sides does a triangle have? What kinds of triangles are there?

WHAT IS A PERPENDICULAR BISECTOR??

PERPENDICULAR BISECTOR Forms right angles. Splits the segment in half

PERPENDICULAR BISECTORS & TRIANGLES Now let’s combine perpendicular bisectors and triangles.

BEGIN BY… Finding the perpendicular bisector of each side of the triangle.

WHAT CAN WE CONCLUDE? What happens when these 3 lines intersect? What is formed?

Perpendicular Bisectors The perpendicular bisectors of a triangle ____________ at a single __________.

EXAMPLE

CIRCUMCENTER The intersection point of the perpendicular bisectors of a triangle

Circumcenter of an Obtuse Triangle

WHAT IS A ANGLE BISECTOR??

ANGLE BISECTOR Splits the angle in half

ANGLE BISECTORS & TRIANGLES Now let’s combine angle bisectors and triangles.

BEGIN BY… Finding the angle bisector of each angle of the triangle.

WHAT CAN WE CONCLUDE? What happens when these 3 lines intersect? What is formed?

Angle Bisector The angle bisectors of a triangle __________ at a single _________.

EXAMPLE

INCENTER The intersection point of the angle bisectors of a triangle

INSCRIBED & CIRCUMSCRIBED CIRCLES

INSCRIBED Inside the triangle Just touches the three sides of the triangle.

INCENTER The center of an inscribed circle Another definition of Incenter: The center of an inscribed circle

CIRCUMSCRIBED Outside the triangle Contains all 3 vertices

CIRCUMCENTER The center of a circumscribed circle

A couple of other definitions you need to know

Altitude A perpendicular line segment from a vertex of a triangle to the line containing the opposite side. How many altitudes can a triangle have?

Median A line segment from a vertex to the midpoint of the opposite side.

Centroid The point where the 3 medians meet