The 5 special segments of a triangle …again Perpendicular bisector Angle bisector Median Altitude Perpendicular and thru a midpoint of a side Bisects an angle Connects vertex to a midpoint Is shortest distance from vertex to opposite side (must be perpendicular)

What are the similarities/differences Altitude Perpendicular Bisector

What are the similarities/differences Median Angle Bisector

The points of concurrency of these 5 special segments

O Is the circumcenter O is equidistant to each Corner of the triangle Where do the tic marks go? The circumcenter is the Point of concurrency of The ______________ Perpendicular Bisectors

J is at the Incenter J The incenter is equidistant to each side Of the triangle So where do we draw congruent Segments from J to a side? Incenter is the point of Concurrency of the… Angle Bisectors

G is at the Centroid Centroid is the point of Concurrency of the medians midpoints The centroid is the center of Gravity of the triangle or “balancing point” Where do we add Tic marks?

H is at the orthocenter The orthocenter is the Point of concurrency Of The Altitudes Each altitude is drawn From a vertex perpendicular To the opposite side

Quick Reference The Perp Bisectors meet at the… The Angle Bisectors meet at the… The medians meet at the … The altitudes meet at the… Circumcenter Incenter Centriod Orthocenter

Is this the circumcenter, incenter,centroid, or orthocenter Incenter Note the angle bisectors

Is this the circumcenter, incenter,centroid, or orthocenter Centroid Note the medians

Is this the circumcenter, incenter,centroid, or orthocenter Orthocenter Note the altitudes

Is this the circumcenter, incenter,centroid, or orthocenter Circumcenter Note the perpendicular Bisectors