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Sec 5-2 and Sec 5-3 Bisectors of Triangles and Medians & Altitudes

Sec 5-2 and Sec 5-3 Bisectors of Triangles and Medians & Altitudes. Concurrency. Point of concurrency. Concurrent Lines (or ray or segments): Three or more lines (or rays or segments ) that intersect in the same point

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Sec 5-2 and Sec 5-3 Bisectors of Triangles and Medians & Altitudes

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  1. Sec 5-2 and Sec 5-3Bisectors of Triangles and Medians & Altitudes

  2. Concurrency Point of concurrency Concurrent Lines (or ray or segments): Three or more lines (or rays or segments) that intersect in the same point Point of Concurrency: The point of intersection of concurrent lines

  3. Theorem: The perpendicular bisectors of the three sides of a triangle meet at one point, called the circumcenter Circumcenter The circumcenter is the center of the circle circumscribed about the triangle

  4. Ex #1: Find the center of a circle that circumscribes about the triangle with vertices at (0,0), (–6, 0), and (0, 4) • • • The circle’s center is located at (–3, 2)

  5. Theorem: The bisectors of the three angles of a triangle meet at one point, called the incenter Incenter The incenter is the center of the circle inscribed inside the triangle

  6. Medians Median – A segment that goes from the vertex of a triangle to the midpoint of the opposite side Centroid All three medians will meet at one point called the centroid

  7. Theorem: The centroid is two-thirds the distance from a vertex of a triangle to the opposite side D G H C F E Ex #2: In the above diagram, JC = 6. Find DC and DJ. J

  8. Altitudes Altitude – A segment that goes from the vertex of a triangle perpendicular to the opposite side The three lines containing the altitudes will meet at one point, called the orthocenter Acute Triangle Right Triangle Obtuse Triangle Orthocenter Orthocenter Orthocenter Orthocenter inside the triangle Orthocenter on the triangle Orthocenter outside the triangle

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