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Segments in Triangles (5.4)

Presentation for Geometry class. Topics include: Medians, Altitudes, Angle Bisectors, Perpendicular Bisectors

Erin Atwood

on 1 November 2012

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Transcript of Segments in Triangles (5.4)

Angle Bisector A ray that divides an angle into two congruent angles Perpendicular Bisector The perpendicular bisector of a segment is a line, segment or ray that is perpendicular to the segment at its midpoint. Concept Summary
Special Segments in Triangles Median A Median of a triangle is a segment whose endpoints are a vertex and the midpoint of the opposite side. Altitude An Altitude is the perpendicular segment from a vertex of a triangle to the line containing the opposite side. 10/26/12 5.4 Medians & Altitudes In any triangle, there are 4 types of special segments: Medians, Altitudes, Angle Bisectors, and Perpendicular Bisectors. Concurrent - always meeting at the same point. A triangle's 3 perpendicular bisectors are always concurrent and meet at the circumcenter. A triangle's 3 angle bisectors are always concurrent and meet at the Incenter. A triangle's 3 medians are always concurrent and meet at the Centroid. Centroid Theorem 2(Median) = 3( Length from Centroid to Vertex) PS=16. Find SM. 16 2(SM)=3(PS) 2(SM)=3(16) 2(SM)=48 SM=24 A triangle's 3 altitudes are always concurrent and meet at the orthocenter. Median Neither Altitude
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