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Special Segments of Triangles

Dive deep into triangle congruence and learn about concurrent lines, points of concurrency, angle bisectors, incenter, perpendicular bisectors, circumcenter, medians, centroids, altitudes, and more. Master the characteristics of special segments within triangles.

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Special Segments of Triangles

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  1. Special Segments of Triangles Advanced Geometry Triangle Congruence Lesson 4

  2. Concurrent Lines 3 or more lines intersect at a common point Point of Concurrency

  3. Angle Bisector Incenter

  4. Perpendicular Bisector passes through the midpoint perpendicular circumcenter

  5. Median vertex midpoint centroid

  6. Altitude vertex perpendicular orthocenter

  7. Characteristics separates an angle in half Special Segment  vertex midpoint   altitude angle bisector     median perpendicular bisector  

  8. Example: If bisects EDF, F = 80, and E = 30, find DGE.

  9. Example: is a perpendicular bisector. If LM = x + 7 and MN = 3x – 11, find the value of x and LN.

  10. Example: is a median, RV = 4x + 9, and VT = 7x – 6. Find the value of x and RV.

  11. THEOREM The centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex on a median.

  12. Example: Points X, Y, and Z are midpoints. Find a, b, and c.

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