1. Points of Concurrency
Triangles

2. Point of Concurrency- ________ or more lines (rays or segments) that intersect are called _____________. The point where they meet is called the “_______of concurrency”
three
concurrent
point
Concurrent lines
Lines that are not concurrent

3. Circumcenter  made from perpendicular bisectors
Circumcenter– all three perpendicular bisectors of a triangle intersect to form a point called a circumcenter.
Fact Equidistant from all three vertices

4. Incenter  made from Angle Bisectors
Incenter – all three angle bisectors of a triangle intersect to form a point called the incenter.
Fact Equidistant to the sides
Distance to sides is vertical

5. Centroid  made from medians
Centroid – all three medians of a triangle intersect to form a point called the centroid.
Fact Vertex to Centroid: /3 total median
Centroid to Midpoint: 1/3 total median

6. Orthocenter  made from altitudes
Orthocenter– all three altitudes of a triangle intersect to form a point called an orthocenter.
Fact Orthocenter can be inside, outside,
or on the right angle.

7. Peter Carried An Important Message Calling All Officers. (PCAIMCAO)
Perpendicular Bisector Circumcenter
Angle Bisector Incenter
Median Centroid
Altitude Orthocenter

8. 10.
Name of Concurrent Point: ______________
Orthocenter
Formed by which segments: _____________
Altitudes

9. 11.
Name of Concurrent Point: ____________
Centroid
Formed by which lines: _____________
Medians

10. 12.
Name of Concurrent Point: ____________
Incenter
Formed by which lines: __________________
Angle Bisectors

11. 13.
Name of Concurrent Point: ___________________
Circumcenter
Formed by which lines:_______________________
Perpendicular Bisectors