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White Note Card: altitude / orthocenter An altitude in a triangle goes through a vertex and is perpendicular to the opposite side. The intersection is the orthocenter of the triangle. orthocenter Location: acute triangle: inside obtuse triangle: outside right triangle: on right angle vertex AE is an altitude. What is true about the diagram? A AE BC Is E a midpoint? BEA and CEA are both right angles. Could E be a midpoint? B E C What is XW? X Z W Y What is an angle bisector? An angle bisector divides an angle into two congruent angles. How many angles are there in a triangle? So, how many angle bisectors are there in a triangle? The intersections of the three angle bisectors in a triangle is called the incenter. Where is the incenter of a triangle located? White Note Card: Angle bisector / incenter An angle bisector in a triangle divides an angle into two congruent angles. The intersection is the incenter of the triangle. It is always inside the triangle. incenter AC is an angle bisector. What is true about the diagram? BAC DAC B Is C a midpoint? C A Is AC BD? D Identify the special segment(s) in each triangle. incenter Classify each triangle described below by angles. If it is not possible to classify the triangle from the information given, then your answer should be “not enough information”. The circumcenter is outside the triangle The circumcenter is on the triangle The incenter is inside the triangle The orthocenter is outside of the triangle The orthocenter is the same as a vertex The centroid is inside the triangle. Circumcenters, centroids, orthocenters, incenters - this is good stuff!