Obj. 22 Triangle Segments
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The document defines and identifies several key segments of triangles including the circumcenter, incenter, altitudes, medians, orthocenter, and centroid. Specifically, it defines the circumcenter as the intersection of the perpendicular bisectors, the incenter as the intersection of the angle bisectors, altitudes as perpendicular segments from vertices to opposite sides, medians as segments from vertices to midpoints of opposite sides, the orthocenter as the intersection of the altitudes, and the centroid as the intersection of the medians.
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Obj. 22 Triangle Segments
- 1. Obj. 22 Triangle Segments The student is able to (I can): • • • • Identify the circumcenter and incenter of a triangle Identify altitudes and medians of triangles Identify the orthocenter and centroid of a triangle Use triangle segments to solve problems
- 2. circumcenter The intersection of the perpendicular bisectors of a triangle.
- 3. circumcenter The intersection of the perpendicular bisectors of a triangle. It is called the circumcenter, because it is the center of a circle that circumscribes the triangle (all three vertices are on the circle).
- 4. incenter The intersection of the angle bisectors of a triangle.
- 5. incenter The intersection of the angle bisectors of a triangle. It is called the incenter because it is the center of the circle that is inscribed in the circle (the circle just touches all three sides).
- 6. median A segment whose endpoints are a vertex of the triangle and the midpoint of the opposite side. altitude A perpendicular segment from a vertex to the line containing the opposite side.
- 7. centroid The intersection of the medians of a triangle. It is also the center of mass for the triangle.
- 8. Centroid Theorem The centroid of a triangle is located of the distance from each vertex to the midpoint of the opposite side. 2 3 H X G 2 GR = GY 3 Y R Z 2 HR = HZ 3 J 2 JR = JX 3
- 9. orthocenter The intersection of the altitudes of a triangle.