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Special Segments in Triangles Lesson 5.2-5.4

Special Segments in Triangles Lesson 5.2-5.4. Special Segments in Triangles. What. YOU"LL LEARN. To identify and use medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle. WHY. IT"S IMPORTANT.

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Special Segments in Triangles Lesson 5.2-5.4

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  1. Special Segments in TrianglesLesson 5.2-5.4

  2. Special Segments in Triangles What YOU"LL LEARN To identify and use medians, altitudes, angle bisectors, and perpendicular bisectors in a triangle. WHY IT"S IMPORTANT You can use the special segments in triangles to solve problems involving engineering, sports, and physics.

  3. Definitions Perpendicular Bisector: A line or line segment that passes through the midpoint of a side of a triangle and is perpendicular to that side.

  4. Definitions Median A segment that connects a vertex of a triangle to the midpoint of the side opposite the vertex.

  5. Definitions Altitude A line segment with 1 endpoint at a vertex of a triangle and the other on the line opposite that vertex so that the line segment is perpendicular to the side of the triangle.

  6. Perp Bisector EquidistanceTHEOREM Any point on a perpendicular bisector of a segment is equidistant from the endpoints of the segment

  7. Converse of PerpEquidistantTHEOREM Any point equidistant from the endpoints of a segment lies on the perpendicular bisector of the segment

  8. EXAMPLE 1 SGB has vertices S(4,7) G(6, 2) and B(12, -1). a. Determine the coordinates of point J on GB so that SJ is a median of SGB . b. Point M has coordinates (8, 3). Is GM an altitude? S . . . M . G J B

  9. L M N J K P O Q EXAMPLE 2 True or False: ON is a median of LOK MP is a median of JLO MO is a perpendicular bisector of JLO

  10. Assignment

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