1. Section 1.5 Special Points in Triangles

2. CONCURRENT
The point where 3 or more lines intersect

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

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

5. WHAT IS A PERPENDICULAR BISECTOR??

6. PERPENDICULAR BISECTOR
Forms right angles.
Splits the segment in half

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

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

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

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

11. EXAMPLE

12. CIRCUMCENTER
The intersection point of the perpendicular bisectors of a triangle

13. Circumcenter of an Obtuse Triangle

14. WHAT IS A ANGLE BISECTOR??

15. ANGLE BISECTOR
Splits the angle in half

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

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

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

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

20. EXAMPLE

21. INCENTER
The intersection point of the angle bisectors of a triangle

22. INSCRIBED & CIRCUMSCRIBED CIRCLES

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

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

25. CIRCUMSCRIBED
Outside the triangle
Contains all 3 vertices

26. CIRCUMCENTER
The center of a circumscribed circle

27. A couple of other definitions you need to know

28. 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?

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

30. Centroid
The point where the 3 medians meet