1. Special Segments in a Triangle

2. When 3 or more lines, rays, or segments intersect in the same pt
When 3 or more lines, rays, or segments intersect in the same pt. this is called the point of concurrency.

3. Median 3 vertex midpoint
A line segment that connects a ___________ to the ____________ of the opposite side.
Every triangle has _________medians
midpoint 3
Draw the picture

4. The intersection of all 3 medians is called the ______________
centroid
Draw the picture ●

5. 3 bisects Angle Bisector
A line segment that ___________ an angle of a triangle.
Every triangle has ________angle bisectors 3
Draw the picture

6. The intersection of all 3 angle bisectors is called _____________
incenter
Draw the picture ●

7. Perpendicular Bisector
midpoint
A line segment that goes through the ____________ of a side and is _________________to that side.
There are _____perpendicular bisectors in a triangle.
perpendicular 3
Draw the picture

8. The point where the 3 perpendicular bisectors meet is called the ________________
circumcenter
draw the picture ●

9. Altitude vertex height 3
A perpendicular segment from its ___________to its opposite side.
It is also known as the ___________.
There are _____altitudes in a triangle.
height 3

10. The point where the 3 altitudes meet is called the _________________
orthocenter ●

11. Medians of a Triangle Theorem
The medians of a triangle intersect at a point that is ⅔ of the distance from each vertex to the midpoint of the opposite side.

13. Copy these in to your journal
Medians of a Triangle Theorem
Angle Bisector Theorem:
The medians of a triangle intersect at a point that is ⅔ of the distance from each vertex to the midpoint of the opposite side.
If a pt. is on the bisector, then it is equidistant from the 2 sides of the angle.
Perpendicular Bisectors Theorem
The perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle

15. Angle Bisector Theorem: If a pt
Angle Bisector Theorem: If a pt. is on the bisector, then it is equidistant from the 2 sides of the angle.

17. Perpendicular Bisectors Theorem
The perpendicular bisector of a triangle intersect at a point that is equidistant from the vertices of the triangle