Points of Concurrency Triangles three or more Point

Points of Concurrency Triangles

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

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

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

Centroid made from medians Centroid – all three medians of a triangle intersect to form a point called the centroid. Fact Vertex to Centroid: 2/3 total median Centroid to Midpoint: 1/3 total median

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.

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

10. Orthocenter Name of Concurrent Point: _______ Altitudes Formed by which segments: _______

11. Name of Concurrent Point: ______ Centroid Formed by which lines: _______ Medians

12. Incenter Name of Concurrent Point: ______ Angle Bisectors Formed by which lines: _________

13. Circumcenter Name of Concurrent Point: __________ Perpendicular Bisectors Formed by which lines: ____________