Section 1.5

Special Points in Triangles

CONCURRENT

• The point where 3 or more lines intersect

TRIANGLES & CIRCLES

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

• How many sides does a triangle have?

• What kinds of triangles are there?

PREVIOUS FACTS…

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??

• Splits the angle in half

ANGLE BISECTOR

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.

• Another definition of Incenter:

• The center of an inscribed circle

INCENTER

CIRCUMSCRIBED

• Outside the triangle

• Contains all 3 vertices

• The center of a circumscribed circle

CIRCUMCENTER

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