11. From any general point on the angle bisector, the perpendicular distance to either side is the same. Why ? P X Y
12. The top angles are congruent by definition of angle bisector. There are two right angles are congruent by def. of perpendicular. P by the reflexive property of = ? ? By AAS X Y By CPCTC
13. Each new point creates 2 congruent triangles by AAS. Why is this important ? Let’s see.
14. P Since the incenter P is on each angle bisector….
15. P Point P is equidistant from each side. Remember, the distance from a point to a line is the brown perpendicular segment. Why is this important? Because these equal distances are radial distances.
16. P The incenter generates an inscribed circle. Radial distances refer to a circle.
29. Obtuse Triangle The lines containing the altitudes are concurrent. The Orthocenter
30. So what do you think is the importance or practical application of the orthocenter is? Nothing !!! It is just an interesting fact that mathematicians have discovered. Isn’t this FUN !!! Psych
31. Summary Line Type Concurrency Point Importance Medians Altitudes Circumcenter Incenter Centroid Orthocenter Equidistant from the vertices Circumscribed Circle Equidistant from the sides Inscribed Circle Center of Balance None
32. C’est fini. Good day and good luck. A Senior Citizen Production That’s all folks.