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The Circumcenter the Incenter the Orthocenter the Centroid This Is A

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The Circumcenter the Incenter the Orthocenter the Centroid This Is A What segment What segment What segment is this? is this? is this? This is a perpendicular bisector. It This is an angle bisector. It bisects This is an altitude. It goes from the is perpendicular to the side and it an angle. vertex and is perpendicular to the bisects that side. (This is shown with the “arc marks” opposite side. Sometimes it may be (This is shown with the “tick marks” on the angles.) outside the triangle. and the perpendicular symbols.) What segment The point of concurrency The point of concurrency is this? for all 3 perpendicular for all 3 angle bisectors bisectors is is This is a median. It goes from the vertex to the midpoint of the The The incenter opposite side. (It bisects the side. This is shown with the “tick marks”.) circumcenter The point of concurrency The point of concurrency Which point of concurrency is for all 3 altitudes is for all 3 medians is this? This is a circumcenter. The The The centroid segments shown are perpendicular bisectors. orthocenter (This is shown with the “tick marks” where the sides are bisected and the perpendicular symbols.) Which point of Which point of Which point of concurrency is concurrency is concurrency is this? this? this? This is an incenter. The segments This is an orthocenter. The This is a centroid. The segments shown are angle bisectors. segments shown are altitudes. shown are medians. (This is shown with the “arc marks” (They are perpendicular but they (The endpoints are at a vertex and where the angles are bisected.) are not bisectors and an endpoint is the midpoint of the opposite sides. at a vertex.) Thus, they bisect the side.) What is a point of What does equidistant The ______ is concurrency? mean? equidistant from all 3 vertices. The point where three When a point is the The or more lines or same distance from circumcenter segments intersect. two or more objects. The ______ is The ______ is two- From a vertex to the equidistant from all 3 thirds of the distance centroid, the distance is sides. from each vertex to the ____ of the median. opposite side. The incenter The centroid What is shown here? From a side to the The ______ is parallel to centroid, the distance is the opposite side and is ____ of the median. half the length of the opposite side Midsegments midsegment Given: ⃗⃗⃗⃗ ⃗ bisects BAC, what is Given: ̅ ̅̅ ̅ ̅ ̅̅ ̅, what is true? Given ⃡ ⃗⃗ ⃗ is a true? perpendicular bisector of ̅ ̅̅ ̅. What is true? BAD CAD ̅̅̅ ̅̅ ̅̅̅ ̅ ̅̅̅ ̅ ̅̅̅ ̅ (of course, it is a bisector!) (of course, it is shown!) More importantly, More importantly, ̅̅̅̅̅ ̅̅̅̅ BAD DAC Given: ̅̅̅ ̅ ̅̅̅ ̅ Which point of Which point of What is true? concurrency is concurrency is shown? shown? ⃡⃗⃗⃗ ⃗ is a perpendicular The incenter. It is the center of The circumcenter. It contains all 3 ̅̅̅̅ the triangle’s inscribed circle . vertices and is circumscribed about bisector of the polygon. AND ̅̅̅ ̅ ̅̅̅ ̅ .
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