1. Geometry Sections 5.2 & 5.3 Points of Concurrency

2. Perpendicular Bisectors Perpendicular Bisectors Intersect to form the Circumcenter, which is the center of the outside circle. Intersect to form the Circumcenter, which is the center of the outside circle. The Circumcenter is equidistant to each of the vertices of the triangle. The Circumcenter is equidistant to each of the vertices of the triangle. The Circumcenter is located in one of three places: The Circumcenter is located in one of three places: –Acute Triangle – Inside the Triangle –Right Triangle – On the Triangle (on the Hypotnuse) –Obtuse Triangle – Outside the Triangle

3. Points of Concurrency Angle Bisectors Angle Bisectors Intersect to form the Incenter, which is the center of the inside circle. Intersect to form the Incenter, which is the center of the inside circle. The Incenter is equidistant to the sides of the triangle. The Incenter is equidistant to the sides of the triangle. The Incenter is always located inside the triangle, regardless of what type it is. The Incenter is always located inside the triangle, regardless of what type it is.

4. Points of Concurrency Median – runs from a vertex to the midpoint of the opposite side. Median – runs from a vertex to the midpoint of the opposite side. Altitude – runs from a vertex and is perpendicular with the opposite side. Altitude – runs from a vertex and is perpendicular with the opposite side.

5. Points of Concurrency Medians Medians Intersect to form the Centroid. Intersect to form the Centroid. From the vertex to the Centroid is 2/3 of the length of the entire median. From the vertex to the Centroid is 2/3 of the length of the entire median. The Centroid is always located inside the triangle, regardless of what type it is. The Centroid is always located inside the triangle, regardless of what type it is.

6. Points of Concurrency Altitudes Altitudes Intersect to form the Orthocenter. Intersect to form the Orthocenter. This creates a bunch of right triangles that you can use the Pythagorean Theorem on. This creates a bunch of right triangles that you can use the Pythagorean Theorem on. The Orthocenter is located in one of three places: The Orthocenter is located in one of three places: –Acute Triangle – Inside the Triangle –Right Triangle – On the Triangle (on vertex of the right angle) –Obtuse Triangle – Outside the Triangle

7. Points of Concurrency LinesPointRule Perpendicular Bisectors Circumcenter (center of outside circle) The circumcenter is equidistant to each of the vertices of the triangle Angle Bisectors Incenter (center of inside circle) The incenter is equidistant to the sides of the triangle MediansCentroid From the vertex to the centroid is 2/3 of the length of the entire median AltitudesOrthocenter No rule – It creates a bunch of right triangles to use the Pythagorean Theorem on

8. Points of Concurrency LinesPointLocation Perpendicular Bisectors Circumcenter (center of outside circle) Acute – Inside Right – On Obtuse - Outside Angle Bisectors Incenter (center of inside circle) Always on inside MediansCentroid AltitudesOrthocenter Acute – Inside Right – On Obtuse - Outside