11From any general point on the angle bisector, the perpendicular distance to either side is the same. Why ?YXP
12The top angles are congruent by definition of angle bisector. There are two right angles are congruent by def. of perpendicular.Yby the reflexive property of =X?By AASP?By CPCTC
13Let’s see. Why is this important ? Each new point creates 2 congruent triangles by AAS.Why is this important ?Let’s see.
14Since the incenter P is on each angle bisector….
15P Why is this important? Point P is equidistant from each side. Remember, the distance from a point to a line is the brown perpendicular segment.PWhy is thisimportant?Because these equal distances are radial distances.
16Radial distances refer to a circle. The incenter generates an inscribed circle.P
17Triangle Points of Concurrency #3Mediansandthe Centroid.
18A median is a segment connecting the vertex to the midpoint of a side of a triangle.
24The birds are tied to their centers of balance or centroids.
25Triangle Points of Concurrency #4Altitudesandthe Orthocenter.
26Acute TriangleThe point of concurrency is called…The Orthocenter
27Right TriangleThe point of concurrency is called…The Orthocenter
28Obtuse TriangleNotice that although the altitudes are not concurrent…
29Obtuse Triangle The Orthocenter The lines containing the altitudes are concurrent.
30So 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.PsychIsn’t this FUN !!!
31Summary None Medians Orthocenter Altitudes Circumcenter Incenter Line TypeConcurrencyPointImportanceEquidistant from the verticesCircumcenterCircumscribed CircleEquidistant from the sidesIncenterInscribed CircleMediansCentroidCenter of BalanceNoneAltitudesOrthocenter
32C’est fini. Good day and good luck. A Senior Citizen Production That’s all folks.A Senior Citizen Production