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**Section 1.5 Special Points in Triangles**

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CONCURRENT The point where 3 or more lines intersect

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

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

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**PREVIOUS FACTS… How many sides does a triangle have?**

What kinds of triangles are there?

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**WHAT IS A PERPENDICULAR BISECTOR??**

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**PERPENDICULAR BISECTOR**

Forms right angles. Splits the segment in half

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**PERPENDICULAR BISECTORS & TRIANGLES**

Now let’s combine perpendicular bisectors and triangles.

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

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

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**Perpendicular Bisectors**

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

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EXAMPLE

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CIRCUMCENTER The intersection point of the perpendicular bisectors of a triangle

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**Circumcenter of an Obtuse Triangle**

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**WHAT IS A ANGLE BISECTOR??**

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ANGLE BISECTOR Splits the angle in half

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**ANGLE BISECTORS & TRIANGLES**

Now let’s combine angle bisectors and triangles.

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

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

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

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EXAMPLE

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INCENTER The intersection point of the angle bisectors of a triangle

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**INSCRIBED & CIRCUMSCRIBED CIRCLES**

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**INSCRIBED Inside the triangle**

Just touches the three sides of the triangle.

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**INCENTER The center of an inscribed circle**

Another definition of Incenter: The center of an inscribed circle

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CIRCUMSCRIBED Outside the triangle Contains all 3 vertices

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CIRCUMCENTER The center of a circumscribed circle

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**A couple of other definitions you need to know**

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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?

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

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Centroid The point where the 3 medians meet

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Perpendicular bisectors and angle bisectors within triangles

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